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Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
4d {N}=2 gauge theories and quivers: the non-simply laced case
NASA Astrophysics Data System (ADS)
Cecotti, Sergio; Del Zotto, Michele
We construct the BPS quivers with superpotential for the 4d {N}=2 gauge theories with non-simply laced Lie groups ( B n , C n , F 4 and G 2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split singular elliptic fibrations. From the categorical viewpoint of arXiv:1203.6734, the fibration of the light category L( {g} ) over the (degenerate) Gaiotto curve has a monodromy given by the action of the outer automorphism of the corresponding unfolded Lie algebra. In view of the Katz-Vafa `matter from geometry' mechanism, the monodromic idea may be extended to the construction of ( Q, W) for SYM coupled to higher matter representations. This is done through a construction we call specialization.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Holographic renormalization group flows in N =3 Chern-Simons-Matter theory from N =3 4D gauged supergravity
NASA Astrophysics Data System (ADS)
Karndumri, Parinya
We study various supersymmetric renormalization group (RG) flows of N =3 Chern-Simons-Matter theory in three dimensions by using four-dimensional N =3 gauged supergravity coupled to eight vector multiplets with S O (3 )×S U (3 ) gauge group. The AdS4 critical point preserving the full S O (3 )×S U (3 ) provides a gravity dual of N =3 superconformal field theory with flavor symmetry S U (3 ). We study the scalar potential and identify a new supersymmetric AdS4 critical point preserving the full N =3 supersymmetry and unbroken S O (3 )×U (1 ) symmetry. An analytic RG flow solution interpolating between S O (3 )×S U (3 ) and S O (3 )×U (1 ) critical points is explicitly given. We then investigate possible RG flows from these AdS4 critical points to nonconformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form AdS2×Σ2 with Σ2 being a two-sphere or a two-dimensional hyperbolic space and find a number of AdS2 geometries preserving four supercharges with S O (2 )×S O (2 )×S O (2 ) and S O (2 )×S O (2 ) symmetries.
Notoph gauge theory: Superfield formalism
NASA Astrophysics Data System (ADS)
Malik, R. P.
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticonimutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.
String Theory and Gauge Theories
Maldacena, Juan
We will see how gauge theories, in the limit that the number of colors is large, give string theories. We will discuss some examples of particular gauge theories where the corresponding string theory is known precisely, starting with the case of the maximally supersymmetric theory in four dimensions which corresponds to ten dimensional string theory. We will discuss recent developments in this area.
Generalized higher gauge theory
NASA Astrophysics Data System (ADS)
Ritter, Patricia; Sämann, Christian; Schmidt, Lennart
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid T M ⊕ T ∗ M over some manifold M and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity
NASA Astrophysics Data System (ADS)
Egawa, H. S.; Horata, S.; Yukawa, T.
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields ( NX) and gauge fields ( NA) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Indepenent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.
Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity
NASA Astrophysics Data System (ADS)
Egawa, H. S.; Horata, S.; Yukawa, T.
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (NX) and gauge fields (NA) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ(4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Indepenent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.
NASA Astrophysics Data System (ADS)
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
We compute the nonzero temperature free energy up to the order g6ln(1/g) in the coupling constant for vectorlike SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Because of large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors, and matter representation. We show that the reduced free energy changes sign, at the second, fifth, and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as a signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g2, agrees with previous predictions for the lower boundary of the conformal window for nonsupersymmetric gauge theories. The higher order results tend to predict a higher number of critical flavors. These are universal properties, i.e. they are independent of the specific matter representation.
Semistrict higher gauge theory
NASA Astrophysics Data System (ADS)
Jurčo, Branislav; Sämann, Christian; Wolf, Martin
We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian tensor multiplet taking values in a semistrict Lie 2-algebra.
Geometry and dynamics of a coupled 4 D-2 D quantum field theory
NASA Astrophysics Data System (ADS)
Bolognesi, Stefano; Chatterjee, Chandrasekhar; Evslin, Jarah; Konishi, Kenichi; Ohashi, Keisuke; Seveso, Luigi
Geometric and dynamical aspects of a coupled 4 D-2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D C{P}^{N-1} zeromodes associated with a nonAbelian vortex become nonnormalizable.
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Silva, Guillermo A.
We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Correa, Diego H.; Silva, Guillermo A.
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Methods of Contemporary Gauge Theory
NASA Astrophysics Data System (ADS)
Makeenko, Yuri
Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.
Methods of Contemporary Gauge Theory
NASA Astrophysics Data System (ADS)
Makeenko, Yuri
Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.
Optical Abelian lattice gauge theories
Tagliacozzo, L.; Celi, A.; Zamora, A.; Lewenstein, M.
We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4 Multiplication-Sign 4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper. - Highlights: Black-Right-Pointing-Pointer We study the quantum simulation of dynamical gauge theories in optical lattices. Black-Right-Pointing-Pointer We focus on digital simulation of abelian lattice gauge theory. Black-Right-Pointing-Pointer We rediscover and discuss the puzzling phase diagram of gauge magnets. Black-Right-Pointing-Pointer We detail the protocol for time evolution and ground-state preparation in any phase. Black-Right-Pointing-Pointer We provide two experimental tests to validate gauge theory quantum simulators.
Progress in lattice gauge theory
Creutz, M.
These lectures first provide an overview of the current status of lattice gauge theory calculations. They then review some technical points on group integration, gauge fixing, and order parameters. Various Monte Carlo algorithms are discussed. Finally, alternatives to the Wilson action are considered in the context of universality for the continuum limit. 41 references.
Quiver gauge theories and integrable lattice models
NASA Astrophysics Data System (ADS)
Yagi, Junya
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity
NASA Astrophysics Data System (ADS)
Hristov, Kiril; Katmadas, Stefanos; Lodato, Ivano
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS2×S2 (or other Riemann surface) preserves half of the supercharges in N = 2 supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture.
Deconfinement Transition and High Temperature Phase in Lattice Gauge Theories
NASA Astrophysics Data System (ADS)
Papa, Alessandro
This paper is organized in two parts. In the first one, I present a recent determination of the critical exponent ν of the correlation length in 3D SU(3) and in 4D SU(2) pure gauge theories at finite temperature, by a new approach inspired by-universality and based on finite size scaling. Moreover, I discuss possible implications of universality on the spectrum of screening masses in 4D SU(2) just above the critical temperature. In the second part, I propose two topics, well known in the literature, to be investigated by numerical simulations on the lattice, namely the Polyakov loop model by Pisarski for the high temperature phase of 4D SU(N) pure gauge theories and the Roberge-Weiss formulation of 4D SU(N) gauge theories with fermions and with imaginary chemical potential.
Gauge theory and chemical structure.
Mattingly, James
The possibility of chemical structure in the context of quantized matter is examined by way of Richard Bader's Atoms in Molecules. I critically examine his notion of "electronic charge density"-showing that he cannot really mean "density of charge"-and I argue that the appropriate concept is expectation value of charge. This still allows him to define chemical structure, but it makes problematic his appeals to the explanatory power of structure. This is because, as Rosenfeld and Bohr showed, the expectation value of charge cannot be taken as the electronic field experienced by other charges. I suggest that we can recover the efficacy of structure by thinking of chemistry as a gauge theory. Current consensus in the study of gauge theories indicates that gauge potentials represent a new type of property; while no member of the family of functions comprising the gauge potential is real, the potential itself is causally potent. I illustrate this in the case of electrodynamics, where the vector potential can causally influence charges in the absence of electric or magnetic fields. I show how chemical structure can be considered to be a gauge field. Following Bader, I take it to be a family of geometric configurations, no one of which is possessed by a given molecule. I claim that current research in gauge theory licenses the attribution of causal potency to this notion of structure, despite its lack of reality. I thus begin the process of freeing the explanatory resources of gauge theory from physics alone. PMID:12796102
Gauge Theories of Vector Particles
DOE R&D Accomplishments Database
Glashow, S. L.; Gell-Mann, M.
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Machines for lattice gauge theory
Mackenzie, P.B.
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig.
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Advances in lattice gauge theory
Duke, D.W.; Owens, J.F.
This book presents papers on advances in lattice gauge theory. Topics covered include fermion Monte Carlo algorithms, portrait of a proton, critical behavior in QCD, the standard Higgs-model on the lattice, analytic calculation of mass gaps, and simulation of discrete Euclidean quantum gravity.
Kreimer, Dirk . E-mail: email@example.com
We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.
On lattice chiral gauge theories
NASA Technical Reports Server (NTRS)
Maiani, L.; Rossi, G. C.; Testa, M.
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.
Introduction to lattice gauge theory
NASA Astrophysics Data System (ADS)
Gupta, R.
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Towards a Neuronal Gauge Theory.
Sengupta, Biswa; Tozzi, Arturo; Cooray, Gerald K; Douglas, Pamela K; Friston, Karl J
Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics--based on approximate Bayesian inference--has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. PMID:26953636
Towards a Neuronal Gauge Theory
Sengupta, Biswa; Tozzi, Arturo; Cooray, Gerald K.; Douglas, Pamela K.; Friston, Karl J.
Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics—based on approximate Bayesian inference—has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. PMID:26953636
Ward identities and gauge independence in general chiral gauge theories
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized Γ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized Γ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.
Gauge anomalies in an effective field theory
Preskill, J. )
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
Superpotentials for Quiver Gauge Theories
Aspinwall, Paul S.; Fidkowski, Lukasz M.; /Stanford U., Phys. Dept.
We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A{sub {infinity}} products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Exts of the quiver and that each such Ext multiplies a polynomial in Exts equal to precisely the relation represented by the Ext.
Gauge theory of glass transition
NASA Astrophysics Data System (ADS)
Vasin, Mikhail
A new analytical approach for the description of the glass transition in a frustrated system is suggested. The theory is based on the non-equilibrium dynamics technique, and takes into account the interaction of the local order field with the massive gauge field, which describes frustration-induced plastic deformation. The glass transition is regarded as a phase transition interrupted because of the premature critical slowing-down of one of the degrees of freedom caused by the frustrations. It is shown that freezing of the system appears when the correlation length and relaxation time of the gauge field diverge. The Vogel-Fulcher-Tammann relation for the transition kinetics and the critical exponent for the nonlinear susceptibility, 2.5\\lesssim \\gamma \\leq 3 , are derived in the framework of the suggested approach. An expression for the temperature dependence of the heat capacity near to the glass transition is derived. This dependence is qualitatively in good agreement with experimental data. The presented theory reproduces the characteristic form of the langphiphirangt correlation function dependence on time, and explains the boson peak appearance on this curve. In addition, the function of the glass transition temperature value with cooling rate is derived; this dependence fully conforms with known experimental data.
Cosmology and unified gauge theory
NASA Astrophysics Data System (ADS)
Oraifeartaigh, L.
Theoretical points in common between cosmology and unified gauge theory (UGT) are reviewed, with attention given to areas of one which have proven useful for the other. The underlying principles for both theoretical frameworks are described, noting the differences in scale, i.e., 10 to the 25th cm in cosmology and 10 to the -15th cm for UGT. Cosmology has produced bounds on the number of existing neutrino species, and also on the mass of neutrinos, two factors of interest in particle physics. Electrons, protons, and neutrinos, having been spawned from the same massive leptons, each composed of three quarks, have been predicted to be present in equal numbers in the Universe by UGT, in line with necessities of cosmology. The Grand UGT also suggests specific time scales for proton decay, thus accounting for the observed baryon assymmetry.
Gauge Coupling Unification in F-Theory Grand Unified Theories
Blumenhagen, Ralph
We investigate gauge coupling unification for F-theory type IIB orientifold constructions of SU(5) grand unified theories (GUT) with gauge symmetry breaking via nontrivial hypercharge flux. This flux has the nontrivial effect that it splits the values of the three minimal supersymmetric standard model gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way.
Gauge coupling unification in F-theory grand unified theories.
Blumenhagen, Ralph
We investigate gauge coupling unification for F-theory type IIB orientifold constructions of SU(5) grand unified theories (GUT) with gauge symmetry breaking via nontrivial hypercharge flux. This flux has the nontrivial effect that it splits the values of the three minimal supersymmetric standard model gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way. PMID:19257658
Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space-time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space-time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space-time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.
Borel Summability of Perturbative Series in 4D N =2 and 5D N =1 Supersymmetric Theories
NASA Astrophysics Data System (ADS)
Honda, Masazumi
We study weak coupling perturbative series in 4D N =2 and 5D N =1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N =2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N =2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.
Gauge theories in terms of invariants
NASA Astrophysics Data System (ADS)
Kijowski, J.; Rudolph, G.; Rudolph, M.
We discuss some aspects of our programme of investigating gauge theories (with fermions) in terms of local gauge invariant quantities. In the first part, the functional integral for quantum electrodynamics is discussed within our formulation. Next, the algebra of Grassmann algebra-valued invariants for one-flavour chromodynamics is investigated and, finally, the functional integral for this theory is derived within our framework.
New identities among gauge theory amplitudes
NASA Astrophysics Data System (ADS)
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
NASA Astrophysics Data System (ADS)
Amariti, Antonio
The reduction of 4d Seiberg duality to 3d by compactification on a circle is possible if finite size effects are considered. These effects boil down to the contribution of KK monopole operators acting as instantons in 3d, and they are crucial to preserve the 4d duality in 3d. This mechanism has been reproduced in string theory by T-duality on the type IIA brane setup. In some cases the 4d dual "magnetic" theories are IR confined descriptions of the UV gauge theories. In these cases the monopoles are absent in the IR dynamics and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also from the "exotic" contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we provide the interpretation of the mechanism in terms of localization.
Curving Yang-Mills-Higgs gauge theories
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
We present a Yang-Mills-Higgs (YMH) gauge theory in which structure constants of the gauge group may depend on Higgs fields. The data of the theory are encoded in the bundle E →M , where the base M is the target space of Higgs fields and fibers carry information on the gauge group. M is equipped with a metric g and E carries a connection ∇. If ∇ is flat, R∇=0 , there is a local field redefinition which gives back the standard YMH gauge theory. If R∇≠0 , one obtains a new class of gauge theories. In this case, contrary to the standard wisdom of the YMH theory, the space (M ,g ) may have no isometries. We build a simple example which illustrates this statement.
A supersymmetric extension of quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Graded geometry in gauge theories and beyond
NASA Astrophysics Data System (ADS)
Salnikov, Vladimir
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using this concept we describe a procedure for analysis of gauge symmetries of given functionals as well as for constructing functionals (sigma models) invariant under an action of some gauge group. As the main example of application of these constructions we consider the twisted Poisson sigma model. We obtain it by a gauging-type procedure of the action of an essentially infinite dimensional group and describe its symmetries in terms of classical differential geometry. We comment on other possible applications of the described concept including the analysis of supersymmetric gauge theories and higher structures.
Dimer models and quiver gauge theories
NASA Astrophysics Data System (ADS)
Pichai, Ramadevi
= 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C are dual to string theories on AdS5×X5 where X5 are Sasaki-Einstein spaces. We present a neat combinatorial approach called dimer model to understand interrelations between toric quiver gauge theories and toric data representing the Calabi-Yau singularities.
Solving flavor puzzles with quiver gauge theories
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)xU(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
Solving flavor puzzles with quiver gauge theories
NASA Astrophysics Data System (ADS)
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)×U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
Lorentz Gauge Theory and Spinor Interaction
NASA Astrophysics Data System (ADS)
Carlevaro, Nakia; Lecian, Orchidea Maria; Montani, Giovanni
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.
Nonperturbative Regulator for Chiral Gauge Theories?
NASA Astrophysics Data System (ADS)
Grabowska, Dorota M.; Kaplan, David B.
We propose a nonperturbative gauge-invariant regulator for d -dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d +1 dimensions with quantum gauge fields that reside on one d -dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d -dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.
Nonperturbative Regulator for Chiral Gauge Theories?
Grabowska, Dorota M; Kaplan, David B
We propose a nonperturbative gauge-invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d+1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter. PMID:27284646
Extracting Flavor from Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Volansky, T.
We consider a large class of models where an SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In particular, under mild assumptions neutrino mass anarchy is predicted.
Numerical techniques for lattice gauge theories
Creutz, M.
The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields.
A lattice formulation of chiral gauge theories
Bodwin, G.T.
We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative problem.
NASA Astrophysics Data System (ADS)
Shi, Yan-Liang; Shrock, Robert
We study asymptotically free chiral gauge theories with an SU (N ) gauge group and chiral fermions transforming according to the antisymmetric rank-k tensor representation, Ak≡[k ]N , and the requisite number, nF ¯, of copies of fermions in the conjugate fundamental representation, F ¯ ≡[1] ¯ N , to render the theories anomaly-free. We denote these as AkF ¯ theories. We take N ≥2 k +1 so that nF ¯≥1 . The A2F ¯ theories form an infinite family with N ≥5 , but we show that the A3F ¯ and A4F ¯ theories are only asymptotically free for N in the respective ranges 7 ≤N ≤17 and 9 ≤N ≤11 , and that there are no asymptotically free AkF ¯ theories with k ≥5 . We investigate the types of ultraviolet to infrared evolution for these AkF ¯ theories and find that, depending on k and N , they may lead to a non-Abelian Coulomb phase, or may involve confinement with massless gauge-singlet composite fermions, bilinear fermion condensation with dynamical gauge and global symmetry breaking, or formation of multifermion condensates that preserve the gauge symmetry. We also show that there are no asymptotically free, anomaly-free SU (N ) SkF ¯ chiral gauge theories with k ≥3 , where Sk denotes the rank-k symmetric representation.
Abelian 3-form gauge theory: Superfield approach
NASA Astrophysics Data System (ADS)
Malik, R. P.
We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).
Noncommutative Gauge Theory with Covariant Star Product
Zet, G.
We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.
Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories
NASA Astrophysics Data System (ADS)
Cvetič, M.; Gubser, S. S.; Lü, H.; Pope, C. N.
A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parametrize the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS6 which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.
Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories
Cvetic, M.; Gubser, S. S.; Lu'', H.; Pope, C. N.
A class of conformally flat and asymptotically anti--de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parametrize the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS{sub 6} which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.
Irregular blocks, N = 2 gauge theory and Mathieu system
NASA Astrophysics Data System (ADS)
Piatek, M. R.; Pietrykowski, A. R.
The Alday-Gayotto-Tachikawa (AGT) conjecture relates 4d N = 2, SU(2) SYM theories with Nf matter hypermultiplets to 2d CFT. In case of pure 4d N = 2, SU(2) SYM there is a corresponding irregular conformal block in 2d CFT. The AGT correspondence may be extended within a certain limit (the Nekrasov-Shataschvili limit) to the correspondence between an effective twisted superpotentials of 2d N = 2 SUSY and the Zamolodchikov's "classical" conformal blocks. When narrowed to the pure 4d N = 2 SYM case its limit is related to an irregular classical conformal block. It will be shown that according to the triple correspondence (2dCFT/Gauge/Bethe - c.f. Piatek's talk) the irregular classical conformal block yields spectrum of Mathieu operator. The latter can be obtained as a "classical" limit of the null vector decoupling equation for three-point degenerate irregular block. It will also be shown that the Mathieu spectrum can be also obtained from the limit of the pure gauge theory as a solution of the saddle point equation as well as from the Bohr-Sommerfeld quantization of the Seiberg-Witten theory.
BPS index and 4d N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Sakai, Kazuhiro
We study the BPS index for the four-dimensional rank-one N = 2 superconformal field theories H 0 , H 1 , H 2 , E 6 , E 7 , E 8. We consider compactifications of the E-string theory on T 2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.
Gauge gravitation theory: Gravity as a Higgs field
NASA Astrophysics Data System (ADS)
Sardanashvily, Gennadi
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.
Central charge bounds in 4D conformal field theory
Rattazzi, Riccardo; Vichi, Alessandro; Rychkov, Slava
We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.
Unifying Geometrical Representations of Gauge Theory
NASA Astrophysics Data System (ADS)
Alsid, Scott; Serna, Mario
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza-Klein theory, those who use Grassmannian models (also called gauge theory embedding or models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school was mostly independently developed, does not compete with other schools, and attempts to isolate the gauge-invariant geometrical surface-like structures that are responsible for the resulting physics. By providing a mapping between geometrical representations, we hope physicists can now isolate representation-dependent physics from gauge-invariant physical results and share results between each school. We provide visual examples of the geometrical relationships between each school for electric and magnetic fields. We highlight a first new result: in all three representations a static electric field (electric field from a fixed ring of charge or a sphere of charge) has a hidden gauge-invariant time dependent surface that is underlying the vector potential.
Scattering processes in lattice gauge theories
NASA Astrophysics Data System (ADS)
Alessandrini, V.; Krzywicki, A.
Scattering between gauge invariant lattice excitations is studied in the framework of a 2+1 dimensional lattice theory with U(1) gauge symmetry. We put the theory in a form analogous to theories of conventional large quantum systems (spin waves in a solid, for example) and we calculate explicitly the cross section for boxiton scattering. The general strategy we have developed goes beyond the simple example of compact QED. Laboratoire associé au CNRS. Postal address: LPTHE, Bâtiment 211, Université Paris-Sud, 91405 Orsay, France.
Origin of gauge invariance in string theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Strominger, A.
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Gauge theories in anti-selfdual variables
NASA Astrophysics Data System (ADS)
Bochicchio, Marco; Pilloni, Alessandro
Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure Yang-Mills from its original definition in = 1 supersymmetric Yang-Mills. We study here the perturbative one-particle irreducible effective action in the anti-selfdual variables of any gauge theory, in particular pure Yang-Mills, QCD and = 1 supersymmetric Yang-Mills. We prove that the one-loop one-particle irreducible effective action of a gauge theory mapped to the anti-selfdual variables in any gauge is identical to the one of the original theory. This is due to the conspiracy between the Jacobian of the change to the anti-selfdual variables and an extra functional determinant that arises from the non-linearity of the coupling of the anti-selfdual curvature to an external source in the Legendre transform that defines the one-particle irreducible effective action. Hence we establish the one-loop perturbative equivalence of the mapped and original theories on the basis of the identity of the one-loop one-particle irreducible effective actions. Besides, we argue that the identity of the perturbative one-particle irreducible effective actions extends order by order in perturbation theory.
Renormalization of gauge theories without cohomology
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
A Gauge Theory of Massive Spin One Particles
NASA Astrophysics Data System (ADS)
Vyas, Vivek M.; Srinivasan, V.
An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.
Minimal Basis for Gauge Theory Amplitudes
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Vanhove, Pierre
Identities based on monodromy for integrations in string theory are used to derive relations between different color-ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color-ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)exclamation amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.
Aspects of entanglement entropy for gauge theories
NASA Astrophysics Data System (ADS)
Soni, Ronak M.; Trivedi, Sandip P.
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories.
Jarzynski's theorem for lattice gauge theory
NASA Astrophysics Data System (ADS)
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
Gauge field theory of covariant strings
NASA Astrophysics Data System (ADS)
Kaku, Michio
We present a gauge covariant second-quantized field theory of strings which is explicitly invariant under the gauge transformations generated by the Virasoro algebra. Unlike the old field theory strings [1] this new formulation is Lorentz covariant as well as gauge covariant under the continuous group Diff( S1) and its central extension. We derive the free action: L=Φ(X) †P[i∂ τ-(L 0-1)]PΦ(X) , in the same way that Feynman derived the Schrödinger equation from the path integral formalism. The action is manifestly invariant under the gauge transformation δΦ(X)= limit∑n=1∞ɛ -nL -nΦ(X) , where P is a projection operator which annihilates spurious states. We give three distinct formulations of this operator P to all orders, the first based on extracting the operator from the functional formulation of the Nambu-Goto action, and the second and third based on inverting the Shapovalov matrix on a Verma module. This gauge covariant formulation can be easily extended to the Green-Schwarz superstring [2,3]. One element application of these methods is to re-express the old Neveu-Schwarz-Ramond model as a field theory which is manifestly invariant under space-time supersymmetric transformations.
Gravity as the square of gauge theory
Bern, Zvi; Dennen, Tristan; Huang Yutin; Kiermaier, Michael
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen, and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By ''squaring'' the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
National Computational Infrastructure for Lattice Gauge Theory
Brower, Richard C.
SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io
Wilson loops in supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Pestun, Vasily
This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.
New Dualities in Supersymmetric Chiral Gauge Theories
Craig, Nathaniel; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F {le} N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F {le} N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.
Computer techniques for lattice gauge theories
NASA Astrophysics Data System (ADS)
Martin, Olivier; Moriarty, K. J. M.; Samuel, Stuart
Quenched SU(3) gauge theory is simulated on a CDC CYBER 205. We describe how to deal with large data sets and discuss the performance of the machine for the two main tasks involved: Monte Carlo updating and Gauss-Seidel inversion.
Supersymmetric instanton calculus (gauge theories with matter)
Vainshtein, A.I.; Zakharov, V.I.; Novikov, V.A.; Shifman, M.A.
We consider instantons in supersymmetric gauge theories with matter. We show that if the vacuum average of the scalar field is different from zero, the number of collective coordinates necessary for describing the matter superfields associated with an instanton changes. We obtain explicit expressions for these superfields. We introduce the concept of an instanton dimension which is invariant with respect to supertransformations.
Quantum critical behavior of semisimple gauge theories
NASA Astrophysics Data System (ADS)
Esbensen, Jacob Kamuk; Ryttov, Thomas A.; Sannino, Francesco
We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an S U (N ) gauge theory with M Dirac flavors where we gauge first an S U (M )L and then an S U (2 )L⊂S U (M )L of the original global symmetry S U (M )L×S U (M )R×U (1 ) of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safety free trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.
Gauge Theory Gravity: Outline and Utility
NASA Astrophysics Data System (ADS)
Francis, Matthew; Kosowsky, Arthur
Gauge Theory Gravity, as formulated by Lasenby, Doran, and Gull, is a reformulation of gravitation as a gauge theory in Minkowski spacetime. This picture makes gravitation look formally analogous to the other forces of nature. It is locally equivalent to general relativity (the basic field equations are equivalent in form to the Cartan formulation of general relativity), but presents significant conceptual differences and certain calculational advantages. We provide an overview of the theory, its explicit relation to general relativity, and outline a constructive method for generating solutions. As an illustration, we obtain the most general spherically symmetric stationary vaccum solution, which explicitly displays all coordinate freedom and contains as special cases all common forms of the spherically symmetric vacuum metric.
Gravity as the Square of Gauge Theory
NASA Astrophysics Data System (ADS)
Kiermaier, M.
The BCJ squaring relations provide a simple prescription for thecomputation of gravity amplitudes in terms of gauge theory ingredients. Unlike the KLT relations, the squaring relations are directly applicable both at tree and loop level. We review the derivation of these relations from on-shell recursion relations, and discuss an off-shell approach to these relations in which the interactions of the gravity Lagrangian arise as the square of the gauge-theory interactions. This article is based on work with Zvi Bern, Tristan Dennen and Yu-tin Huang [Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Phys. Rev. D textbf{82} (2010), 065003, arXiv:1004.0693 (Ref. 1))] which was presented at String Field Theory and Related Aspects 2010.
Passing to an effective 4D phantom cosmology from 5D vacuum theory of gravity
NASA Astrophysics Data System (ADS)
Aguilar, José Edgar Madriz; Bellini, Mauricio
Starting from a five-dimensional (5D) vacuum theory of gravity where the extra coordinate is considered as non-compact, we investigate the possibility of inducing four-dimensional (4D) phantom scenarios by applying form-invariance symmetry transformations. In particular we obtain phantom scenarios for two cosmological frameworks. In the first framework we deal with an induced 4D de Sitter expansion and in the second one a 4D induced model where the expansion of the universe is dominated by a decreasing cosmological parameter Λ(t) is discussed.
Strong dynamics and lattice gauge theory
NASA Astrophysics Data System (ADS)
Schaich, David
In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses
Quantum walks and discrete gauge theories
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Debbasch, Fabrice
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
Light-Front Quantization of Gauge Theories
Brodskey, Stanley
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Stringy Instantons and Quiver Gauge Theories
Florea, Bogdan; Kachru, Shamit; McGreevy, John; Saulina, Natalia
We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (''instantons'') that intersect space-filling D-branes. These effects can perturb the effective field theory on the space-filling branes by nontrivial operators composed of charged matter fields, changing the vacuum structure in a qualitative way in some examples. Our considerations are exemplified throughout by a careful study of a fractional brane configuration on a del Pezzo surface.
Strong Coupling Gauge Theories in LHC ERA
NASA Astrophysics Data System (ADS)
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
AdS/QCD, light-front holography, and the nonperturbative running coupling / Stanley J. Brodsky, Guy de Teramond and Alexandre Deur -- New results on non-abelian vortices - Further insights into monopole, vortex and confinement / K. Konishi -- Study on exotic hadrons at B-factories / Toru Iijima -- Cold compressed baryonic matter with hidden local symmetry and holography / Mannque Rho -- Aspects of baryons in holographic QCD / T. Sakai -- Nuclear force from string theory / K. Hashimoto -- Integrating out holographic QCD back to hidden local symmetry / Masayasu Harada, Shinya Matsuzaki and Koichi Yamawaki -- Holographic heavy quarks and the giant Polyakov loop / Gianluca Grignani, Joanna Karczmarek and Gordon W. Semenoff -- Effect of vector-axial-vector mixing to dilepton spectrum in hot and/or dense matter / Masayasu Harada and Chihiro Sasaki -- Infrared behavior of ghost and gluon propagators compatible with color confinement in Yang-Mills theory with the Gribov horizon / Kei-Ichi Kondo -- Chiral symmetry breaking on the lattice / Hidenori Fukaya [for JLQCD and TWQCD collaborations] -- Gauge-Higgs unification: Stable Higgs bosons as cold dark matter / Yutaka Hosotani -- The limits of custodial symmetry / R. Sekhar Chivukula ... [et al.] -- Higgs searches at the tevatron / Kazuhiro Yamamoto [for the CDF and D[symbol] collaborations] -- The top triangle moose / R. S. Chivukula ... [et al.] -- Conformal phase transition in QCD like theories and beyond / V. A. Miransky -- Gauge-Higgs unification at LHC / Nobuhito Maru and Nobuchika Okada -- W[symbol]W[symbol] scattering in Higgsless models: Identifying better effective theories / Alexander S. Belyaev ... [et al.] -- Holographic estimate of Muon g - 2 / Deog Ki Hong -- Gauge-Higgs dark matter / T. Yamashita -- Topological and curvature effects in a multi-fermion interaction model / T. Inagaki and M. Hayashi -- A model of soft mass generation / J. Hosek -- TeV physics and conformality / Thomas Appelquist -- Conformal
Anomaly nucleation constrains SU(2) gauge theories.
Halverson, James
We argue for the existence of additional constraints on SU(2) gauge theories in four dimensions when realized in ultraviolet completions admitting an analog of D-brane nucleation. In type II string compactifications these constraints are necessary and sufficient for the absence of cubic non-Abelian anomalies in certain nucleated SU(N>2) theories. It is argued that they appear quite broadly in the string landscape. Implications for particle physics are discussed; most realizations of the standard model in this context are inconsistent, unless extra electroweak fermions are added. PMID:24483790
Spinning black holes in a gauge theory of gravitation
NASA Astrophysics Data System (ADS)
Babeţi (Pretorian), Simona
Spinning black holes are presented in terms of gauge fields in a commutative gauge theory of gravitation. The field strength tensor comes as a consequence of the particular ansatz for gauge fields. In order to obtain spinning black holes in a noncommutative gauge theory of gravitation is used an analytical procedure conceived in GRTensorII. To calculate the leading noncommutative corrections and to choose an appropriate noncommutative parameter are used recursive relations. The gauge fields and the field strength tensor for a spinning mass preserves some features of other cosmological solutions in the gauge theory of gravitation and the noncommutative corrections are expected to provide some important physical insights.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
NASA Astrophysics Data System (ADS)
Taylor, Washington; Wang, Yi-Nan
We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ˜ 1048. The distribution of bases peaks around h 1,1 ˜ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in h 1,1 of the threefold base. Typical bases have ˜ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) × SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) × SU(2) is the third most common connected two-factor product group, following SU(2) × SU(2) and G 2 × SU(2), which arise more frequently.
Monte Carlo methods in lattice gauge theories
Otto, S.W.
The mass of the O/sup +/ glueball for SU(2) gauge theory in 4 dimensions is calculated. This computation was done on a prototype parallel processor and the implementation of gauge theories on this system is described in detail. Using an action of the purely Wilson form (tract of plaquette in the fundamental representation), results with high statistics are obtained. These results are not consistent with scaling according to the continuum renormalization group. Using actions containing higher representations of the group, a search is made for one which is closer to the continuum limit. The choice is based upon the phase structure of these extended theories and also upon the Migdal-Kadanoff approximation to the renormalizaiton group on the lattice. The mass of the O/sup +/ glueball for this improved action is obtained and the mass divided by the square root of the string tension is a constant as the lattice spacing is varied. The other topic studied is the inclusion of dynamical fermions into Monte Carlo calculations via the pseudo fermion technique. Monte Carlo results obtained with this method are compared with those from an exact algorithm based on Gauss-Seidel inversion. First applied were the methods to the Schwinger model and SU(3) theory.
Gauge theories under incorporation of a generalized uncertainty principle
Kober, Martin
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
Perturbative gauge theory at null infinity
NASA Astrophysics Data System (ADS)
Adamo, Tim; Casali, Eduardo
We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.
Lattice gauge theories and Monte Carlo algorithms
Creutz, M.
Lattice gauge theory has become the primary tool for non-perturbative calculations in quantum field theory. These lectures review some of the foundations of this subject. The first lecture reviews the basic definition of the theory in terms of invariant integrals over group elements on lattice bonds. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. The second lecture turns to numerical simulation, which has become an important approach to calculating hadronic properties. Here I discuss the basic algorithms for obtaining appropriately weighted gauge field configurations. The third lecture turns to algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. 34 refs.
Continuum regularization of gauge theory with fermions
Chan, H.S.
The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Fernández-Melgarejo, J. J.; Rosseel, Jan; Townsend, Paul K.
We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schrödinger model.
Black hole attractors and gauge theories
NASA Astrophysics Data System (ADS)
Huang, Lisa Li Fang
This thesis is devoted to the study of supersymmetric black holes that arise from string compactifications. We begin by studying the R 2 corrections to the entropy of two solutions of five dimensional supergravity, the supersymmetric black ring and the spinning black hole. Using Wald's formula we compute the R2 corrections to the entropy of the black ring and BMPV black hole. We study N D4-branes wrapping a 4 cycle and M DO-branes on the quintic. For N D4-branes, we resolve the naive mismatch between the moduli space of the Higgs branch of the gauge theory and the moduli of a degree N hypersurface which the D4-brane wraps. The degree N surface must admit a holomorphic divisor and is a determinantal variety. Adding a single DO brane to probe the deformed geometry, we recover the determinant equation from F and D flatness condition which was previously discovered from a classical geometry approach. We next generalize the qunitic story for Calabi-Yau manifolds arising from complete intersections in toric varieties. We recover the moduli space of N D4-branes in terms of the moduli space of a U( N) x U(N) gauge theory with bi-fundamentals com ing from a D6 - D6 system. We also recast the tachyon condensation of the D6 - D6 system in the language of open string gauged linear sigma model. We obtain the determinant equation from F-term constraints arising from a boundary coupling. We set out to understand the Ooguri-Strominger-Vafa conjecture directly in the D4-DO black hole attractor geometry. We show that the lift to the euclidean IIA attractor geometry gives a complexified M-theory geometry whose asymptotic boundary is a torus. Employing AdS3/CFT 2 duality, we argue that the string partition function computes the elliptic genus of the Maldacena-Strominger-Witten conformal field theory. We evaluate the IIA partition function using the Green-Schwarz formalism and show that it gives ZtopZ top, coming from instantons and anti-instantons respectively. Finally, we determine
CP nonconservation in dynamically broken gauge theories
Lane, K.
The recent proposal of Eichten, Lane, and Preskill for CP nonconservation in electroweak gauge theories with dynamical symmetry breaking is reviewed. Through the alignment of the vacuum with the explicit chiral symmetry breaking Hamiltonian, these theories provide a natural way to understand the dynamical origin of CP nonconservation. Special attention is paid to the problem of strong CP violation. Even through all vacuum angles are zero, this problem is not automatically avoided. In the absence of strong CP violation, the neutron electric dipole moment is expected to be 10/sup -24/-10/sup -26/ e-cm. A new class of models is proposed in which both strong CP violation and large /..delta..S/ = 2 effects may be avoided. In these models, /..delta..C/ = 2 processes such as D/sup o/ D/sup -o/ mixing may be large enough to observe.
Probing the ground state in gauge theories
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.; Lutz, W.
We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the nonabelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.
The Origins of Lattice Gauge Theory
Wilson, Kenneth
The main focus of this talk is an anecdotal account of the history underlying my 1974 article entitled 'Confinement of Quarks.' In preparing this talk, I will draw on a historical interview conducted by the project for History of Recent Science and Technology at the Dibner Institute for the History of Science and Technology at MIT, and on a theory of invention proposed by Peter Drucker in his book 'Innovation and Entrepreneurship.' I will explain this theory; no background is needed. The account will start with related work in the 1960's. I will end the talk with a plea for lattice gauge researchers to be alert for unexpected scalar or vector colored particles that are invisible to experimentalists yet could start to spoil the agreement of computations with experiment. Note: In association with the Symposium ' 'Lattice 2004,' June 21 to June 26, 2004.
Towards gauge theories in four dimensions
NASA Astrophysics Data System (ADS)
Hernández-Pinto, Roger J.; Sborlini, Germán F. R.; Rodrigo, Germán
The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.
a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Malik, R. P.
We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
Coupled Cluster Methods in Lattice Gauge Theory
NASA Astrophysics Data System (ADS)
Watson, Nicholas Jay
Available from UMI in association with The British Library. Requires signed TDF. The many body coupled cluster method is applied to Hamiltonian pure lattice gauge theories. The vacuum wavefunction is written as the exponential of a single sum over the lattice of clusters of gauge invariant operators at fixed relative orientation and separation, generating excitations of the bare vacuum. The basic approximation scheme involves a truncation according to geometrical size on the lattice of the clusters in the wavefunction. For a wavefunction including clusters up to a given size, all larger clusters generated in the Schrodinger equation are discarded. The general formalism is first given, including that for excited states. Two possible procedures for discarding clusters are considered. The first involves discarding clusters describing excitations of the bare vacuum which are larger than those in the given wavefunction. The second involves rearranging the clusters so that they describe fluctuations of the gauge invariant excitations about their self-consistently calculated expectation values, and then discarding fluctuations larger then those in the given wavefunction. The coupled cluster method is applied to the Z_2 and Su(2) models in 2 + 1D. For the Z_2 model, the first procedure gives poor results, while the second gives wavefunctions which explicitly display a phase transition with critical couplings in good agreement with those obtained by other methods. For the SU(2) model, the first procedure also gives poor results, while the second gives vacuum wavefunctions valid at all couplings. The general properties of the wavefunctions at weak coupling are discussed. Approximations with clusters spanning up to four plaquettes are considered. Excited states are calculated, yielding mass gaps with fair scaling properties. Insight is obtained into the form of the wavefunctions at all couplings.
S-folds and 4d mathcal{N} = 3 superconformal field theories
NASA Astrophysics Data System (ADS)
Aharony, Ofer; Tachikawa, Yuji
S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by García-Etxebarria and Regalado to provide the first construction of four dimensional mathcal{N} =3 superconformal theories. In this note, we classify the different variants of these mathcal{N} =3-preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of mathcal{N} =3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.
The Higgs sector of gravitational gauge theories
Leclerc, M. . E-mail: email@example.com
Gravitational gauge theories with de Sitter, Poincare and affine symmetry group are investigated under the aspect of the breakdown of the initial symmetry group down to the Lorentz subgroup. As opposed to the nonlinear realization approach, in the dynamical symmetry breaking procedure, the structure subgroup is not chosen arbitrarily, but is dictated by the symmetry of the groundstate of a Higgs field. We review the theory of spontaneously broken de Sitter gravity by Stelle and West and apply a similar approach to the case of the Poincare and affine groups. We will find that the Poincare case is almost trivial. The translational Higgs field reveals itself as pure gauge, i.e., it is expressed entirely in terms of the Nambu-Goldstone bosons and does not appear in the Lagrangian after the symmetry breaking. The same holds for the translational part of the affine group. The Higgs field provoking the breakdown of the general linear group leads to the determination of the Lorentzian signature of the metric in the groundstate. We show that the Higgs field remains in its groundstate, i.e., that the metric will have Lorentzian signature, unless we introduce matter fields that explicitely couple to the symmetric part of the connection. Furthermore, we present arguments that the Lorentzian signature is actually the only possible choice for physical spacetime, since the symmetry breaking mechanism works only if the stability subgroup is taken to be the Lorentz group. The other four-dimensional rotation groups are therefore ruled out not only on physical, but also on theoretical grounds. Finally, we show that some features, like the necessity of the introduction of a dilaton field, that seem artificial in the context of the affine theory, appear most natural if the gauge group is taken to be the special linear group in five dimensions. We also present an alternative model which is based on the spinor representation of the Lorentz group and is especially adopted to the
We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Generating functionals for Green's functions in gauge field theories
Bordag, M.; Kaschlun, L.; Matveev, V.A.; Robaschik, D.
The structure of the generating functional of the one-particle-irreducible Green's functions in gauge field theories is investigated. Both axial as well as covariant gauge conditions are considered. For both cases, the general structure of the functionals is obtained, and a functional expansion with respect to nonlocal operators is given. The appearance of gauge-dependent operators in the case of the covariant gauge follows in a natural manner from the structure of the corresponding functional.
Conformal field theory dual of the RS model with gauge fields in the bulk
NASA Astrophysics Data System (ADS)
Agashe, K.; Delgado, A.
It has been conjectured that the (weakly coupled) Randall-Sundrum (RS) model with gauge fields in the bulk is dual to a (strongly coupled) 4D conformal field theory (CFT) with an UV cutoff and in which global symmetries of the CFT are gauged. We elucidate features of this dual CFT which are crucial for a complete understanding of the proposed duality. We argue that the limit of no (or small) brane-localized kinetic term for bulk gauge field on the RS side (often studied in the literature) is dual to no bare kinetic term for the gauge field which is coupled to the CFT global current. In this limit, the kinetic term for this gauge field in the dual CFT is "induced" by CFT loops. Then, this CFT loop contribution to the gauge field 1PI two-point function is dual (on the RS side) to the full gauge propagator (i.e., including the contribution of Kaluza-Klein and zero modes) with both external points on the Planck brane. We also emphasize that loop corrections to the gauge coupling on the RS side are dual to subleading effects in a large-N expansion on the CFT side; these subleading corrections to the gauge coupling in the dual CFT are (in general) sensitive to the strong dynamics of the CFT.
Nonquadratic gauge fixing and ghosts for gauge theories on the hypersphere
NASA Astrophysics Data System (ADS)
Brandt, F. T.; McKeon, D. G. C.
It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this nonquadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.
Nonquadratic gauge fixing and ghosts for gauge theories on the hypersphere
Brandt, F. T.; McKeon, D. G. C.
It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this nonquadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.
Hydrodynamic gradient expansion in gauge theory plasmas.
Heller, Michal P; Janik, Romuald A; Witaszczyk, Przemysław
We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a 'nonhydrodynamic' quasinormal mode on the gravity side. PMID:23745858
The renormalon diagram in gauge theories on
NASA Astrophysics Data System (ADS)
Anber, Mohamed M.; Sulejmanpasic, Tin
We analyze the renormalon diagram of gauge theories on . In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel between the vacuum part and finite volume part, which eliminates the IR renormalon problem. We argue that the singularities in the Borel plane, arising from the topological neutral bions, are not associated with the renormalon diagram, but with the proliferation of the Feynman diagrams. As a byproduct, we obtain, for the first time, an exact one-loop result of the vacuum polarization which can be adapted to the case of thermal compactification of QCD.
Application of unified array calculus to connect 4-D spacetime sensing with string theory and relativity
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
Array algebra of photogrammetry and geodesy unified multi-linear matrix and tensor operators in an expansion of Gaussian adjustment calculus to general matrix inverses and solutions of inverse problems to find all, or some optimal, parametric solutions that satisfy the available observables. By-products in expanding array and tensor calculus to handle redundant observables resulted in general theories of estimation in mathematical statistics and fast transform technology of signal processing. Their applications in gravity modeling and system automation of multi-ray digital image and terrain matching evolved into fast multi-nonlinear differential and integral array calculus. Work since 1980's also uncovered closed-form inverse Taylor and least squares Newton-Raphson-Gauss perturbation solutions of nonlinear systems of equations. Fast nonlinear integral matching of array wavelets enabled an expansion of the bundle adjustment to 4-D stereo imaging and range sensing where real-time stereo sequence and waveform phase matching enabled data-to-info conversion and compression on-board advanced sensors. The resulting unified array calculus of spacetime sensing is applicable in virtually any math and engineering science, including recent work in spacetime physics. The paper focuses on geometric spacetime reconstruction from its image projections inspired by unified relativity and string theories. The collinear imaging equations of active object space shutter of special relativity are expanded to 4-D Lorentz transform. However, regular passive imaging and shutter inside the sensor expands the law of special relativity by a quantum geometric explanation of 4-D photogrammetry. The collinear imaging equations provide common sense explanations to the 10 (and 26) dimensional hyperspace concepts of a purely geometric string theory. The 11-D geometric M-theory is interpreted as a bundle adjustment of spacetime images using 2-D or 5-D membrane observables of image, string and
Parity anomalies in gauge theories in 2 + 1 dimensions
Rao, S.; Yahalom, R.
We show that the introduction of massless fermions in an abelian gauge theory in 2+1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarization tensor. However, parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry. 6 refs.
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Emmenegger, N.
In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.
National Computational Infrastructure for Lattice Gauge Theory
Reed, Daniel, A
In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantim chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the serior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is pubicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice guage theorists in the United States on a peer reviewed basis.
Chern-Simons gauge theory: Ten years after
Labastida, J. M. F.
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach.
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
SDiff gauge theory and the M2 condensate
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; Townsend, Paul K.
We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its Script N = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff2 super-Yang-Mills theory describing a condensate of D2-branes.
Ward-Takahashi identities for Abelian chiral gauge theories
NASA Astrophysics Data System (ADS)
de Lima, Ana Paula Cardoso Rodrigues; Dias, Sebastião Alves
By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward-Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.
Evidence for a Family of SO(8) Gauged Supergravity Theories
NASA Astrophysics Data System (ADS)
Dall'Agata, G.; Inverso, G.; Trigiante, M.
In this note we discuss the classification of duality orbits of N=8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings, and the scalar potential are parameter dependent. We also comment on the possible M theory uplift and on the meaning of the parameter for the dual gauge theories.
Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories
NASA Astrophysics Data System (ADS)
Chandra, Nitin
This is my PhD thesis. In this thesis we study the gauge theories on noncommutative Moyal space. We find new static solitons and instantons in terms of the so called generalized Bose operators. Generalized Bose operators are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of generalized Bose operators. The Nielsen-Olesen vortex solutions found in terms of these operators reduce to the already found ones. On the contrary we find a class of new instaton solutions which are unitarily inequivalant to the the ones found from ADHM construction on noncommutative space. The charge of the instaton has a description in terms of the index representing the reducibility of the Fock space, i.e., k. After studying the static solitonic solutions in noncommutative Minkowski space and the instaton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also try to understand the implications of the found results in the context of quantum optics. We then shift to the so called DSR theories which are related to a different kind of noncommutative (kappa-Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
Investigation of gauge-fixed pure U(1) theory at strong coupling
NASA Astrophysics Data System (ADS)
Basak, S.; De, Asit K.
We numerically investigate the phase diagram of pure U(1) gauge theory with gauge fixing at strong gauge coupling. The FM-FMD phase transition, which proved useful in defining Abelian lattice chiral gauge theory, persists also at strong gauge coupling. However, there the transition seems no longer to be continuous. At large gauge couplings we find evidences for confinement.
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Scattering amplitudes in gauge theories: progress and outlook Scattering amplitudes in gauge theories: progress and outlook
NASA Astrophysics Data System (ADS)
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
Phase diagram of 4D field theories with chiral anomaly from holography
NASA Astrophysics Data System (ADS)
Ammon, Martin; Leiber, Julian; Macedo, Rodrigo P.
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Two-color gauge theory with novel infrared behavior.
Appelquist, T; Brower, R C; Buchoff, M I; Cheng, M; Fleming, G T; Kiskis, J; Lin, M F; Neil, E T; Osborn, J C; Rebbi, C; Schaich, D; Schroeder, C; Syritsyn, S; Voronov, G; Vranas, P; Witzel, O
Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived nonperturbatively from the Schrödinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings g(2) of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in nonsupersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior. PMID:24702347
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the "scale-space." We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
U([infinity]) gauge theory from higher dimensions
Shiraishi, K. )
In this paper, the authors show that classical U[infinity] gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the infinite-dimensional symmetry can be taken as spontaneously broken. Monopole solutions are examined in the model for scalar and gauge fields. An extension to gravity is also discussed.
SU{sub {ital q}}(2) lattice gauge theory
Bimonte, G.; Stern, A.; Vitale, P.
We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, the symmetry gets promoted to a quantum group gauge symmetry. The theory depends on two parameters: the deformation parameter {lambda} and the lattice spacing {ital a}. We show that the system of Kogut and Susskind is recovered when {lambda}{r_arrow}0, while QCD is recovered in the continuum limit (for any {lambda}). We, thus, have the possibility of having a two-parameter regularization of QCD. {copyright} {ital 1996 The American Physical Society.}
Second-Order Gauge Invariant Cosmological Perturbation Theory --- Einstein Equations in Terms of Gauge Invariant Variables ---
NASA Astrophysics Data System (ADS)
Nakamura, K.
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
Gauge theory of Virasoro-Kac-Moody group
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Zoh, S. W.
We present a prototype gauge theory of the Virasoro-Kac-Moody symmetry associated with an arbitrary grand unified group G, which could be interpreted as an effective field theory of a colored string. The theory automatically breaks the symmetry down to H⊗U(1), where H is a subgroup of G and U(1) is the Cartan subgroup of the Virasoro group. After the inevitable spontaneous symmetry breaking the particle spectrum of the theory consists of an infinite tower of massive spin-one fields, the massless gauge fields of the unbroken subgroup, and the light scalar fields which become the pseudo-Goldstone fields of the symmetry breaking
Loop calculus for lattice gauge theories
Gambini, R.; Leal, L.; Trias, A.
Hamiltonian calculations are performed using a loop-labeled basis where the full set of identities for the SU(/ital N/) gauge models has been incorporated. The loops are classified as clusterlike structures and the eigenvalue problem leads to a linear set of finite-difference equations easily amenable to numerical treatment. Encouraging results are reported for SU(2) at spatial dimension 2.
Relational mechanics as a gauge theory
NASA Astrophysics Data System (ADS)
Ferraro, Rafael
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the resulting equations of motion are valid in any frame. The compensating terms provide inertial forces depending on the total momentum P, intrinsic angular momentum J and intrinsic inertia tensor I. Therefore, the privileged frames where Newton's equations are valid ( Newtonian frames) are completely determined by the matter distribution of the universe ( Machianization). At the Hamiltonian level, the gauge invariance leads to first class constraints that remove those degrees of freedom that make no sense once the absolute space has been eliminated. This reformulation of classical mechanics is entirely relational, since it is a dynamics for the distances between particles. It is also Machian, since the rotation of the rest of the universe produces centrifugal effects. It then provides a new perspective to consider the foundational ideas of general relativity, like Mach's principle and the weak equivalence principle. With regard to the concept of time, the absence of an absolute time is known to be a characteristic of parametrized systems. Furthermore, the scale invariance of those parametrized systems whose potentials are inversely proportional to the squared distances can be also gauged by introducing another compensating term associated with the intrinsic virial G ( shape-dynamics).
The M-theory origin of global properties of gauge theories
NASA Astrophysics Data System (ADS)
Amariti, Antonio; Klare, Claudius; Orlando, Domenico; Reffert, Susanne
We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN-1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.
Dynamics of N = 2 Supersymmetric Gauge Theories in Three Dimensions
de Boer, J.; Hori, K.; Oz, Y.
We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N{sub c}) and SU(N{sub c}) with N{sub f} flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.
Ward identities and renormalization of general gauge theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
We introduce the concept of general gauge theory which includes Yang-Mills models. We use the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields. For the Yang-Mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid. The investigation of higher orders of the perturbation theory is still an open problem.
Gauge theories on hyperbolic spaces and dual wormhole instabilities
Buchel, Alex
We study supergravity duals of strongly coupled four-dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicate establishing the precise gauge theory/string theory correspondence dictionary. These backgrounds suffer from the nonperturbative instabilities arising from the D3D3-bar pair-production in the background four-form potential. We discuss conditions for suppressing this Schwingerlike instability. We find that Euclidean wormholes arising in this construction develop a naked singularity before they can be stabilized.
Thermodynamics of quasiconformal theories from gauge/gravity duality
Alanen, Janne; Kajantie, Keijo; Tuominen, Kimmo
We use gauge/gravity duality to study the thermodynamics of a generic almost conformal theory, specified by its beta function. Three different phases are identified, a high temperature phase of massless partons, an intermediate quasiconformal phase and a low temperature confining phase. The limit of a theory with infrared fixed point, in which the coupling does not run to infinity, is also studied. The transitions between the phases are of first order or continuous, depending on the parameters of the beta function. The results presented follow from gauge/gravity duality; no specific boundary theory is assumed, only its beta function.
Gauging nonrelativistic field theories using the coset construction
NASA Astrophysics Data System (ADS)
Karananas, Georgios K.; Monin, Alexander
We discuss how nonrelativistic spacetime symmetries can be gauged in the context of the coset construction. We consider theories invariant under the centrally extended Galilei algebra as well as the Lifshitz one, and we investigate under what conditions they can be supplemented by scale transformations. We also clarify the role of torsion in these theories.
Variational Study of SU(3) Gauge Theory by Stationary Variance
NASA Astrophysics Data System (ADS)
Siringo, Fabio
The principle of stationary variance is advocated as a viable variational approach to gauge theories. The method can be regarded as a second-order extension of the Gaussian Effective Potential (GEP) and seems to be suited for describing the strong-coupling limit of non-Abelian gauge theories. The single variational parameter of the GEP is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of coupled integral equations. The stationary conditions can be easily derived by the self-energy, without having to write the effective potential, making use of a general relation between self-energy and functional derivatives that has been proven to any order. The low- energy limit of pure Yang-Mills SU(3) gauge theory has been studied in Feynman gauge, and the stationary equations are written as integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.
Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds
NASA Astrophysics Data System (ADS)
Ghilencea, Dumitru M.; Lee, Hyun Min; Schmidt-Hoberg, Kai
We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional Script N = 1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k2) and the effective gauge coupling geff(k2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of geff(k2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of geff(k2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.
Cosmologies with null singularities and their gauge theory duals
Das, Sumit R.; Michelson, Jeremy; Narayan, K.; Trivedi, Sandip P.
We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in S. R. Das, J. Michelson, K. Narayan, S. P. Trivedi, hep-th/0602107. The dual theory is a deformed N=4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a lightlike direction. We concentrate on backgrounds which become AdS{sub 5}xS{sup 5} at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the matrix membrane theory which describes these pp-wave backgrounds.
Monte Carlo simulations of lattice gauge theories
Rebbi, C
Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)
Dualities between semiclassical strings and quantum gauge field theories
NASA Astrophysics Data System (ADS)
Ouyang, Peter
In this thesis we study several examples of the correspondence between gauge field theories and string theories. A recurrent theme of these studies is that distinctively quantum mechanical behavior on the gauge theory side of the correspondence can have a classical or semiclassical description in terms of string calculations, as one might expect from general considerations of open/closed duality. We begin in Chapter 1 by reviewing the simplest duality, which relates Type IIB supergravity in AdS5 x S5 to N = 4 SU(N) gauge theory at large N. Working with this background spacetirne, we turn to a study of D-brane probes with large quantum numbers in Chapter 2. We employ semiclassical methods to compute the excitation spectrum of these D-branes, including corrections of order 1/N, which are related to loop effects in the dual field theory. In Chapter 3 we discuss the gauge/gravity duals with N = 1 supersymmetry which arise from placing D-branes at a conifold singularity. The inclusion of fractional D3-branes breaks conformal invariance, leading to a rich variety of phenomena in the gauge theory, among them chiral anomalies, a cascade of Seiberg dualities and confinement in the infrared. We pay particular attention to the chiral anomalies of the gauge theory and show that they can be described in terms of classical spontaneous symmetry breaking in the dual string theory. In accord with low-energy confinement in the field theory, almost all of the moduli of the supergravity solution are fixed; we conclude Chapter 3 with some observations on the possibility of stabilizing the volume of the compact space in which the conifold is embedded. Finally, in Chapter 4 we study versions of the conifold theory with D7-branes, which introduce fundamental matter into the gauge theory. By solving the classical supergravity equations of motion we identify a variant of the Klebanov-Strassler duality cascade where the rate of the cascade decreases as the theory flows to low energies.
Conformal gauge-Yukawa theories away from four dimensions
NASA Astrophysics Data System (ADS)
Codello, Alessandro; Langæble, Kasper; Litim, Daniel F.; Sannino, Francesco
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d = 4 + ɛ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD d and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.
Towards a gauge theory interpretation of the real topological string
NASA Astrophysics Data System (ADS)
Hayashi, Hirotaka; Piazzalunga, Nicolò; Uranga, Angel M.
We consider the real topological string on certain noncompact toric Calabi-Yau three-folds X , in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol'nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.
Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory
NASA Astrophysics Data System (ADS)
Pinto, Carlos
We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.
This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.
Conformally flat black holes in Poincaré gauge theory
NASA Astrophysics Data System (ADS)
Blagojević, M.; Cvetković, B.
General criteria for the existence of conformally flat Riemannian solutions in three-dimensional Poincaré gauge theory without matter are formulated. Using these criteria, we show that the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend gravity, is also an exact vacuum solution of the Poincaré gauge theory. The related conserved charges, calculated from the Hamiltonian boundary term, are shown to satisfy the first law of black hole thermodynamics. The form of the boundary term is verified by using the covariant Hamiltonian approach.
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
Gauges and functional measures in quantum gravity I: Einstein theory
NASA Astrophysics Data System (ADS)
Ohta, N.; Percacci, R.; Pereira, A. D.
We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family of gauges. Trying to reduce the gauge- and measure-dependence selects certain classes of measures and gauges respectively. There is a choice of two parameters (corresponding to the exponential parametrization and the partial gauge condition that the quantum field be traceless) that automatically eliminates the dependence on the remaining two parameters and on the cosmological constant. We observe that the divergences are invariant under a Z 2 "duality" transformation that (in a particularly important special case) involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. This singles out a formulation of unimodular gravity as the unique "self-dual" theory in this class.
Massive gravity as a quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F+ (Hgraviton) where the one-particle Hilbert space Hgraviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space Hgraviton generated by the gravitational field hμν and some ghosts fields uμ, ũμ (which are vector Fermi fields) and vμ (which is a vector Bose field).
Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory
Ydri, Badis
We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two plaquettes. This equivalence holds in the 'fuzzy sphere' phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the matrix phase we have a U(N) gauge theory on a single point.
Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces
NASA Astrophysics Data System (ADS)
Ishibashi, Nobuyuki; Murakami, Koichi
It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.
Gauge transformation of double field theory for open string
NASA Astrophysics Data System (ADS)
Ma, Chen-Te
We combine symmetry structures of ordinary (parallel directions) and dual (transversal directions) coordinates to construct the Dirac-Born-Infeld theory. The ordinary coordinates are associated with the Neumann boundary conditions and the dual coordinates are associated with the Dirichlet boundary conditions. Gauge fields become scalar fields by exchanging the ordinary and dual coordinates. A gauge transformation of a generalized metric is governed by the generalized Lie derivative. The gauge transformation of the massless closed string theory gives the C -bracket, but the gauge transformation of the open string theory gives the F -bracket. The F -bracket with the strong constraints is different from the Courant bracket by an exact one-form. This exact one-form should come from the one-form gauge field. Based on a symmetry point of view, we deduce a suitable action with a nonzero H -flux at the low-energy level. From an equation of motion of the scalar dilaton, it defines a generalized scalar curvature. Finally, we construct a double sigma model with a boundary term and show that this model with constraints is classically equivalent to the ordinary sigma model.
Noncommutative gauge theory and symmetry breaking in matrix models
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3){sub c}xSU(2){sub L}xU(1){sub Q}[resp. SU(3){sub c}xU(1){sub Q}], which couples appropriately to all fields in the standard model. An additional U(1){sub B} gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.
Regularized path integrals and anomalies: U(1) chiral gauge theory
NASA Astrophysics Data System (ADS)
Kopper, Christoph; Lévêque, Benjamin
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Guimaraes, M. S.; Mintz, B. W.; Sorella, S. P.
We investigate the dimension two condensate ⟨ϕ¯ia bϕia b-ω¯ia bωia b⟩ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate ⟨ϕ¯i a bϕia b-ω¯i a bωia b⟩ is plagued by a nonintegrable IR divergence in 3 D , while in 4 D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter γ2. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.
Gauge theory of disclinations on fluctuating elastic surfaces
NASA Astrophysics Data System (ADS)
Kochetov, E. A.; Osipov, V. A.
A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in 0305-4470/32/10/013/img1 may vary. Moreover, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadic gauge theory is obtained. Within the linear scheme our model recovers the von Karman equations for membranes, with a disclination-induced source being generated by gauge fields. For a single disclination on an arbitrary elastic surface a covariant generalization of the von Karman equations is derived.
BRST detour quantization: Generating gauge theories from constraints
Cherney, D.; Waldron, A.; Latini, E.
We present the Becchi-Rouet-Stora-Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kaehler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kaehler electromagnetism. We also discuss how our results generalize to other special geometries.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Ohberg, Patrik
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle vector potential corresponds to a constant synthetic magnetic field. We find a new type of current non-linearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate on the physical conditions that make the nucleation of a quantized vortex in the system energetically favourable with respect to the non rotating solution. Two different physical interpretations can be given to this new non linearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. We analyze the physical conditions that make a single vortex state energetically favourable. In the Thomas-Fermi limit, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating depends on the density of the cloud. The authors acknowledge support from CM-DTC and EPSRC.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current nonlinearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas-Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new nonlinearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.
Coulomb branches for rank 2 gauge groups in 3 d N=4 gauge theories
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Sperling, Marcus
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Exponentiation of eikonal cross sections in nonabelian gauge theories
NASA Astrophysics Data System (ADS)
Gatheral, J. G. M.
A theorem is presented which generalises the well-known exponentiation property of eikonal cross sections in abelian gauge theories to the nonabelian case. Address after September 1, 1983: Bank of America, 25 Cannon Street, London EC4P 4HN, UK.
Finite-Temperature Gauge Theory from the Transverse Lattice
Dalley, S.; Sande, B. van de
Numerical computations are performed and analytic bounds are obtained on the excited spectrum of glueballs in SU({infinity}) gauge theory, by transverse lattice Hamiltonian methods. We find an exponential growth of the density of states, implying a finite critical (Hagedorn) temperature. It is argued that the Nambu-Goto string model lies in a different universality class.
Hamiltonian flow in Coulomb gauge Yang-Mills theory
Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel
We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.
Spatial Dependence of Condensates in Strongly Coupled Gauge Theories
Brodsky, Stanley J.; Shrock, Robert; /SUNY, Stony Brook
We analyze quark and gluon condensates in quantum chromodynamics. We suggest that these are localized inside hadrons, because the particles whose interactions are responsible for them are confined within these hadrons. This can explain the results of recent studies of gluon condensate contributions to vacuum correlators. We also give a general discussion of condensates in asymptotically free vectorial and chiral gauge theories.
Nonlocal Hamiltonian gauge theories and their connection with lattice Hamiltonians
Ktorides, C.N.; Mavromatos, N.E.
We introduce the concept of primitive Hamiltonian density for nonlocal Abelian gauge theories. We subsequently study the local limit both with respect to the continuum and with respect to a lattice structure introduced via hypercubic cells. The non-Abelian case is also discussed.
A gauge theory of gravity in curved phase-spaces
NASA Astrophysics Data System (ADS)
Castro, Carlos
After a cursory introduction of the basic ideas behind Born's Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann-Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the 8D cotangent bundle T∗M of spacetime is explicitly constructed and based on the gauge group SO(6, 2) ×sR8 which acts on the tangent space to the cotangent bundle T(x,p)T∗M at each point (x,p). Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.
Weighted power counting and Lorentz violating gauge theories. II: Classification
Anselmi, Damiano
We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are usually non-renormalizable, such as the two scalar-two fermion interactions and the four fermion interactions. A number of four-dimensional examples are presented.
Gauge theories from D7-branes over vanishing 4-cycles
Franco, Sebastian; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.
On a gauge covariant formulation of string field theories
NASA Astrophysics Data System (ADS)
Ju-Fei, Tang; Chuan-Jie, Zhu
It is shown that the Neveu-Nicolai-West formulation of the gauge covariant string field theories and that of Banks and Peskin can be obtained by different consistent truncation of the BRST multiplets. A proof is given to show the equivalence of light-cone formulation and the gauge covariant formulation without using the property of trivial cohomology of string differential forms. We would like to thank D.D. Wu and X.J. Zhou for discussion and Yi-Bing Ding for careful reading of the manuscript.
Sasakian quiver gauge theories and instantons on the conifold
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.; Lechtenfeld, Olaf; Popov, Alexander D.; Szabo, Richard J.
We consider Spin (4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form Md ×T 1 , 1, where Md is a smooth manifold and T 1 , 1 is a five-dimensional Sasaki-Einstein manifold Spin (4) / U (1). We obtain new quiver gauge theories on Md extending those induced via reduction over the leaf spaces CP1 × CP1 in T 1 , 1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin (4)-equivariant instantons on the conifold which is realized as the metric cone over T 1 , 1. We give an explicit construction of these moduli spaces as Kähler quotients.
Spontaneous parity violation and SUSY strong gauge theory
Haba, Naoyuki; Ohki, Hiroshi
We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest new models. Our models show confinement, so that we try to understand them by using a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. This structure has several advantages compared to the MSSM. The scale of the Higgs mass (left-right breaking scale) and that of VEVs are different, so the SUSY little hierarchy problems are absent. The second model also induces spontaneous supersymmetry breaking.
Grand unified string theories with SU(3) gauge family symmetry
NASA Astrophysics Data System (ADS)
Maslikov, A. A.; Sergeev, S. M.; Volkov, G. G.
In the framework of four dimensional heterotic superstring with free fermions we investigate the rank eight Grand Unified String Theories (GUST) which contain the SU(3) H-gauge family symmetry. We explicitly construct GUSTs with gauge symmetry G = SU(5) × U(1) × ( SU(3) × U(1)) H ⊂ SO(16) ⊂ E(8) in free complex fermion formulation. We solve the problem of the GUST symmetry breaking taking for the observable gauge symmetry the diagonal subgroup Gsym of rank 16 group G × G ⊂ SO(16) × SO(16) ⊂ E(8) × E(8). In this approach the observed electromagnetic charge Qem can be viewed as a sum of two Q1- and Q2-charges of each G-group. In this case the model spectrum does not contain particles with exotic fractional charges.
Vortex dynamics in superfluids governed by an interacting gauge theory
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik
We study the dynamics of a vortex in a quasi two-dimensional Bose gas consisting of light-matter coupled atoms forming two-component pseudo spins. The gas is subject to a density dependent gauge potential, hence governed by an interacting gauge theory, which stems from a collisionally induced detuning between the incident laser frequency and the atomic energy levels. This provides a back-action between the synthetic gauge potential and the matter field. A Lagrangian approach is used to derive an expression for the force acting on a vortex in such a gas. We discuss the similarities between this force and the one predicted by Iordanskii, Lifshitz and Pitaevskii when scattering between a superfluid vortex and the thermal component is taken into account.
Microscopic quantum superpotential in Script N = 1 gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
We consider the Script N = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of Script N = 2 super Yang-Mills theories to the realm of Script N = 1 gauge theories.
Lattice Gauge Theory for Nuclear Physics
Konstantinos Orginos
Quantum Chromodynamcs (QCD) is now established as the theory of strong interactions. A plethora of hadronic physics phenomena can be explained and described by QCD. From the early days of QCD, it was clear that low energy phenomena require a non-perturbative approach. Lattice QCD is a non-perturbative formulation of QCD that is particularly suited for numerical calculations. Today, supercomputers have achieved performance cabable of performing calculations that allow us to understand complex phenomana that arise from QCD. In this talk I will review the most recent results, relevant to nuclear physics. In particular, I will focus on results relevant to the structure and interactions of hadrons. Finally, I will comment on the opportunities opening up as we approach the era of exaflop computing.
Brane webs in the presence of an O5--plane and 4 d class S theories of type D
NASA Astrophysics Data System (ADS)
Zafrir, Gabi
In this article we conjecture a relationship between 5 d SCFT's, that can be engineered by 5-brane webs in the presence of an O5--plane, and 4 d class S theories of type D. The specific relation is that compactification on a circle of the former leads to the latter. We present evidence for this conjecture. One piece of evidence, which is also an interesting application of this, is that it suggests identifications between different class S theories. This can in turn be tested by comparing their central charges.
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Phases of N=1 Supersymmetric Chiral Gauge Theories
Craig, Nathaniel; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
We analyze the phases of supersymmetric chiral gauge theories with an antisymmetric tensor and (anti)fundamental flavors, in the presence of a classically marginal superpotential deformation. Varying the number of flavors that appear in the superpotential reveals rich infrared chiral dynamics and novel dualities. The dualities are characterized by an infinite family of magnetic duals with arbitrarily large gauge groups describing the same fixed point, correlated with arbitrarily large classical global symmetries that are truncated nonperturbatively. At the origin of moduli space, these theories exhibit a phase with confinement and chiral symmetry breaking, an interacting nonabelian Coulomb phase, and phases where an interacting sector coexists with a sector that either s-confines or is in a free magnetic phase. Properties of these intriguing 'mixed phases' are studied in detail using duality and a-maximization, and the presence of superpotential interactions provides further insights into their formation.
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
Boucher-Veronneau, C.; Dixon, L.J.; /SLAC
We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
Flavor Gauge Theory, and Masses of Top and Neutrino
NASA Astrophysics Data System (ADS)
Cvetič, G.; Kim, C. S.
We assume that the standard model (SM) breaks down around some energy Λ, and is replaced by a new (Higgsless) flavor gauge theory (FGT). We investigate this possibility by studying the renormalization group equations for the Yukawa couplings of SM with two Higgs doublets for various mt and υU/υD. With appropriate flavor democratic boundary conditions at ΛFGT, we derive the bounds on masses of top and tau-neutrino, which are compatible with experimental bounds.
Gauge-invariant cosmological perturbation theory with seeds
Durrer, R. )
Gauge-invariant cosmological perturbation theory is extended to handle perturbations induced by seeds. A calculation of the Sachs-Wolfe effect is presented. A second-order differential equation for the growth of density perturbations is derived and the perturbation of Liouville's equation for collisionless particles is also given. The results are illustrated by a simple analytic example of a single texture knot, where we calculate the induced perturbations of the energy of microwave photons, of baryonic matter, and of collisionless particles.
Gauge approach to gravitation and regular Big Bang theory
NASA Astrophysics Data System (ADS)
Minkevich, A. V.
Field theoretical scheme of regular Big Bang in 4-dimensional physical space-time, built in the framework of gauge approach to gravitation, is discussed. Regular bouncing character of homogeneous isotropic cosmological models is ensured by gravitational repulsion effect at extreme conditions without quantum gravitational corrections. The most general properties of regular inflationary cosmological models are examined. Developing theory is valid, if energy density of gravitating matter is positive and energy dominance condition is fulfilled.
Enhanced gauge symmetry and winding modes in double field theory
NASA Astrophysics Data System (ADS)
Aldazabal, G.; Graña, M.; Iguri, S.; Mayo, M.; Nuñez, C.; Rosabal, J. A.
We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1) × U(1) symmetry to SU(2) × SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with Oleft(d+3,d+3right)/Oleft(d+3right)× Oleft(d+3right) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.
Gauge theory, topological strings, and S-duality
NASA Astrophysics Data System (ADS)
Kapustin, Anton
We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa. We deduce it from the S-duality of the IIB superstring. We also argue that the mirror version of this duality relates the topological B-model on a Calabi-Yau 3-fold and a topological sector of the Type IIA Little String Theory on the same manifold.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
[Investigations in dynamics of gauge theories in theoretical particle physics
Not Available
The major theme of the theoretical physics research conducted under DOE support over the past several years has been within the rubric of the standard model, and concerned the interplay between symmetries and dynamics. The research was thus carried out mostly in the context of gauge field theories, and usually in the presence of chiral fermions. Dynamical symmetry breaking was examined both from the point of view of perturbation theory, as well as from non-perturbative techniques associated with certain characteristic features of specific theories. Among the topics of research were: the implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in any theory, topological and conformal properties of quantum fields in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD, the phenomenological implications of a strongly interacting Higgs sector in the standard model, and the application of soliton ideas to the physics to be explored at the SSC.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Local gauge transformation for the quark propagator in an SU(N) gauge theory
NASA Astrophysics Data System (ADS)
Aslam, M. Jamil; Bashir, A.; Gutiérrez-Guerrero, L. X.
In an S U (N ) gauge field theory, the n -point Green functions, namely, propagators and vertices, transform under the simultaneous local gauge variations of the gluon vector potential and the quark matter field in such a manner that the physical observables remain invariant. In this article, we derive this intrinsically nonperturbative transformation law for the quark propagator within the system of covariant gauges. We carry out its explicit perturbative expansion up to O (gs6) and, for some terms, up to O (gs8) . We study the implications of this transformation for the quark-antiquark condensate, multiplicative renormalizability of the massless quark propagator, as well as its relation with the quark-gluon vertex at the one-loop order. Setting the color factors CF=1 and CA=0 , Landau-Khalatnikov-Fradkin transformation for the Abelian case of quantum electrodynamics is trivially recovered. We also test whether the usually employed proposals for the truncations of Schwinger-Dyson equations are consistent with what the Landau-Khalatnikov-Fradkin transformations entail for the massless quark propagator.
D-branes, gauge/string duality and noncommutative theories
NASA Astrophysics Data System (ADS)
Mateos, Toni
In this thesis we elaborate on the three subjects of the title. We first show that supertubes exist and still preserve some supersymmetry in a large variety of curved backgrounds. Within the AdS/CFT correspondence we study the supersymmetry of rotating strings with 3 angular momenta, and we consider the possibility of adding matter in a stable but non-supersymmetric way. We contribute to the extension of the duality to more realistic YM theories by constructing the sugra dual of an N=2 pure SYM in 3d, given in terms of a Calabi-Yau four-fold in M-theory. We study the unitarity of noncommutative nonrelativistic field theories, we construct the sugra dual of noncommutative pure SYM theories with N=1 in 4d and N=2 in 3d, and we study holographically properties like UV/IR mixing, confinement, chiral symmetry breaking and moduli spaces.
On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
Naot, Gad
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semisimple one by taking its semidirect product with its Lie algebra. We find that the standard knot observable (i.e., trace of the holonomy along the knot) essentially vanishes, and yet, the non-semi-simplicity of the gauge group allows us to consider a class of unorthodox observables which breaks gauge invariance at one point and leads to a nontrivial theory on long knots in R{sup 3}. We have two main morals. (1) In the non-semi-simple case there is more to observe in Chern-Simons theory. There might be other interesting non-semi-simple gauge groups to study in this context beyond our example. (2) In the case of an inhomogeneous gauge group, we find that Chern-Simons theory with the unorthodox observable is actually the same as three-dimensional BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. We prove that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.
A combinatorial approach to diffeomorphism invariant quantum gauge theories
Zapata, J.A.
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in {ital separable} Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. {copyright} {ital 1997 American Institute of Physics.}
Two-dimensional lattice gauge theories with superconducting quantum circuits
Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Two-dimensional lattice gauge theories with superconducting quantum circuits
Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability. PMID:25512676
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
New fuzzy extra dimensions from S U (N ) gauge theories
NASA Astrophysics Data System (ADS)
Kürkçüoǧlu, Seçkin
We start with an S U (N ) Yang-Mills theory on a manifold M , suitably coupled to scalar fields in the adjoint representation of S U (N ) , which are forming a doublet and a triplet, respectively, under a global S U (2 ) symmetry. We show that a direct sum of fuzzy spheres SF2 Int≔SF2(ℓ)⊕SF2(ℓ)⊕SF2(ℓ+1/2 )⊕SF2(ℓ-1/2 ) emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and paves the way for us to interpret the spontaneously broken model as a U (n ) gauge theory over M ×SF2 Int . Focusing on a U (2 ) gauge theory, we present complete parametrizations of the S U (2 )-equivariant, scalar, spinor and vector fields characterizing the effective low energy features of this model. Next, we direct our attention to the monopole bundles SF2 ±≔SF2(ℓ)⊕SF2(ℓ±1/2 ) over SF2(ℓ) with winding numbers ±1 , which naturally come forth through certain projections of SF2 Int , and give the parametrizations of the S U (2 )-equivariant fields of the U (2 ) gauge theory over M ×SF2 ± as a projected subset of those of the parent model. Referring to our earlier work [1], we explain the essential features of the low energy effective action that ensues from this model after dimensional reduction. Replacing the doublet with a k -component multiplet of the global S U (2 ), we provide a detailed study of vacuum solutions that appear as direct sums of fuzzy spheres as a consequence of the spontaneous breaking of S U (N ) gauge symmetry in these models and obtain a class of winding number ±(k -1 )∈Z monopole bundles SF2 ,±(k -1 ) over SF2(ℓ) as certain projections of these vacuum solutions and briefly discuss their equivariant field content. We make the observation that SF2 Int is indeed the bosonic part of the N =2 fuzzy supersphere with O S P (2 ,2 ) supersymmetry and construct the generators of the o s p (2 ,2 ) Lie superalgebra in two of its irreducible representations using the matrix content of the vacuum solution SF2 Int
Yang-Mills Gauge Theory and Higgs Particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU (2) × SU (3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Yang-Mills gauge theory and Higgs particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU(2) × SU(3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Simple U (1 ) gauge theory explanation of the diphoton excess
NASA Astrophysics Data System (ADS)
Chang, Spencer
The recent ATLAS and CMS diphoton resonance excesses are explored in a simple U (1 ) gauge theory extension of the Standard Model where the resonance is the Higgs boson of the U (1 ) symmetry breaking, ϕ . This particle couples to exotic quarks which, through loops, can produce a large enough rate to explain the excess. Due to the choice of U (1 ) charges, flavor constraints are naturally suppressed, allowing arbitrary flavor violation in the decays of the new quarks to up-type quarks, modifying their signal topologies. An additional heavy quark in the model decays to the lighter exotic quark by emitting either ϕ or the U (1 ) gauge boson Ax, giving extra signals containing diphoton and digluon resonances. Finally, the new Higgs can decay into γ Ax and Z Ax, followed by Ax decaying into Standard Model fermions through kinetic mixing. Thus, this model gives interesting modified signals to the general class of exotic quark models explaining the diphoton resonance.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Search for a Minimal N =1 Superconformal Field Theory in 4D
NASA Astrophysics Data System (ADS)
Xie, Dan; Yonekura, Kazuya
We discuss a candidate for a minimal interacting four-dimensional N =1 superconformal field theory. The model contains a chiral primary operator u satisfying the chiral ring relation u2=0 , and its scaling dimension is Δ (u )=1.5 . The model is derived by turning on a N =1 preserving deformation of N =2 A2 Argyres-Douglas theory. The central charges are given by (a ,c )=(263 /768 ,271 /768 )≃(0.342 ,0.353 ) . There is no moduli space of vacua, no flavor symmetry, and the chiral ring is finite.
Classical irregular block, = 2 pure gauge theory and Mathieu equation
NASA Astrophysics Data System (ADS)
Piątek, Marcin; Pietrykowski, Artur R.
Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U{sub A}(1) symmetry and the {eta}{prime} for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
Andreev, Oleg
We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range. PMID:19519096
Classical probes of string/gauge theory duality
NASA Astrophysics Data System (ADS)
Ishizeki, Riei
The AdS/CFT correspondence has played an important role in the recent development of string theory. The reason is that it proposes a description of certain gauge theories in terms of string theory. It is such that simple string theory computations give information about the strong coupling regime of the gauge theory. Vice versa, gauge theory computations give information about string theory and quantum gravity. Although much is known about AdS/CFT, the precise map between the two sides of the correspondence is not completely understood. In the unraveling of such map classical string solutions play a vital role. In this thesis, several classical string solutions are proposed to help understand the AdS/CFT duality. First, rigidly rotating strings on a two-sphere are studied. Taking special limits of such solutions leads to two cases: the already known giant magnon solution, and a new solution which we call the single spike solution. Next, we compute the scattering phase shift of the single spike solutions and compare the result with the giant magnon solutions. Intriguingly, the results are the same up to non-logarithmic terms, indicating that the single spike solution should have the same rich spin chain structure as the giant magnon solution. Afterward, we consider open string solutions ending on the boundary of AdS5. The lines traced by the ends of such open strings can be viewed as Wilson loops in N = 4 SYM theory. After applying an inversion transformation, the open Wilson loops become closed Wilson loops whose expectation value is consistent with previously conjectured results. Next, several Wilson loops for N = 4 SYM in an AdS5 pp-wave background are considered and translated to the pure AdS 5 background and their interpretation as forward quark-gluon scattering is suggested. In the last part of this thesis, a class of classical solutions for closed strings moving in AdS3 x S 1 ⊂ AdS5 x S5 with energy E and spin S in AdS3 and angular momentum J and winding m
Monopole Condensation and Confining Phase of N=1 Gauge Theories Via M Theory Fivebrane
de Boer, Jan; Oz, Yaron
The fivebrane of M theory is used in order to study the moduli space of vacua of confining phase N=1 supersymmetric gauge theories in four dimensions. The supersymmetric vacua correspond to the condensation of massless monopoles and confinement of photons. The monopole and meson vacuum expectation values are computed using the fivebrane configuration. The comparison of the fivebrane computation and the field theory analysis shows that at vacua with a classically enhanced gauge group SU(r) the effective superpotential obtained by the"integrating in" method is exact for r=2 but is not exact for r> 2. The fivebrane configuration corresponding to N=1 gauge theories with Landau-Ginzburg type superpotentials is studied. N=1 non-trivial fixed points are analyzed using the brane geometry.
Naturalness and ultraviolet structure of gauge theories with massive fermions
NASA Astrophysics Data System (ADS)
Gellas, G. C.; Karanikas, A. I.; Ktorides, C. N.
According to the principle of naturalness a small, with respect to the cutoff, mass parameter entering a quantum field system is natural only when it is compatible with some symmetry in the limit where it vanishes. In this paper, advantage is taken of the liberty afforded by the renormalization procedure in order to harmonize the cutoff with the physical mass in a non-Abelian gauge field theory with spin-1/2 matter fields. The ultraviolet structure of the theory, from such a vantage point, is explored at the level of the full fermionic propagator, as well as the vertex function, using the world line approach. An interplay between this ultraviolet structure and the infrared behavior of the same system, but from the customary viewpoint ``cutoff much greater than mass,'' is pointed out. Direct implications for open fermionic lines in the world line path integral casting of field theories are also made.
Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory
NASA Astrophysics Data System (ADS)
Gupta, S.; Kumar, R.; Malik, R. P.
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated ( B∧ F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.
Lattice gaugefixing and other optics in lattice gauge theory
Yee, Ken.
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Orbifold family unification in SO(2N) gauge theory
Kawamura, Yoshiharu; Miura, Takashi
We study the possibility of family unification on the basis of SO(2N) gauge theory on the five-dimensional space-time, M{sup 4}xS{sup 1}/Z{sub 2}. Several SO(10), SU(4)xSU(2){sub L}xSU(2){sub R}, or SU(5) multiplets come from a single bulk multiplet of SO(2N) after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.
Perturbative vacuum wavefunctional for gauge theories in the Milne space
NASA Astrophysics Data System (ADS)
Jeon, Sangyong; Epelbaum, Thomas
The spectrum of vacuum fluctuations in the Milne space (i.e. the τ - η coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrödinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method (Dusling et al., 2011; Epelbaum and Gelis, 2013).
Lattice Gauge Theory and the Origin of Mass
Kronfeld, Andreas S.
Most of the mass of everyday objects resides in atomic nuclei/ the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons---protons and neutrons---whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via $M=E/c^2$, that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
Campagnari, Davide R.; Reinhardt, Hugo; Weber, Axel
We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static color sources are calculated to one-loop order. Furthermore, the one-loop {beta} function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.
Finite and Gauge-Yukawa unified theories: Theory and predictions
Kobayashi, T.; Kubo, J.; Mondragon, M.; Zoupanos, G.
All-loop Finite Unified Theories (FUTs) are very interesting N=1 GUTs in which a complete reduction of couplings has been achieved. FUTs realize an old field theoretical dream and have remarkable predictive power. Reduction of dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exists RGI relations among dimensionless couplings that guarantee the vanishing of the {beta}- functions in certain N=1 supersymmetric GUTS even to all orders. Recent developments in the soft supersymmetry breaking (SSB) sector of N=1 GUTs and FUTs lead to exact RGI relations also in this sector of the theories. Of particular interest is a RGI sum rule for the soft scalar masses holding to all orders. The characteristic features of SU(5) models that have been constructed based on the above tools are: a) the old agreement of the top quark prediction with the measured value remains unchanged, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above several hundreds of GeV.
Geometry and topology of bubble solutions from gauge theory
NASA Astrophysics Data System (ADS)
Chen, Heng-Yu; Correa, Diego H.; Silva, Guillermo A.
We study how geometrical and topological aspects of certain (1)/(2)-BPS type IIB supergravity solutions are captured by the N=4 super Yang-Mills gauge theory in the AdS/CFT context. The type IIB solutions are completely characterized by arbitrary droplets in a plane and we consider, in particular, concentric droplets. We probe the dual (1)/(2)-BPS operators of the gauge theory with single traces and extract their one-loop anomalous dimensions. The action of the one-loop dilatation operator can be reformulated as the Hamiltonian of a bosonic lattice. The operators defining the Hamiltonian encode the topology of the droplet. The axial symmetry of the droplets turns out to be essential for obtaining the spectrum of the Hamiltonians. In appropriate BMN limits, the near-BPS spectrum reproduces the spectrum of near-BPS string excitations propagating along each individual edge of the droplet of the dual geometric background. We also study semiclassical regimes for the Hamiltonians. We show that, for droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
AGT relations for abelian quiver gauge theories on ALE spaces
NASA Astrophysics Data System (ADS)
Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.
We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
Exact WKB analysis of {N} = 2 gauge theories
NASA Astrophysics Data System (ADS)
Ashok, Sujay K.; Jatkar, Dileep P.; John, Renjan R.; Raman, M.; Troost, Jan
We study {N} = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by ɛ 1- and ɛ 2-deformed instanton partition functions. We confirm their validity at leading order in ɛ 2 via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of ɛ 1-deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of ɛ 1 is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.
/N=2 gauge theories from wrapped five-branes
NASA Astrophysics Data System (ADS)
Bigazzi, F.; Cotrone, A. L.; Zaffaroni, A.
We present string duals of four-dimensional N=2 pure SU(N) SYM theory. The theory is obtained as the low energy limit of D5-branes wrapped on non-trivial two-cycles. Using seven-dimensional gauged supergravity and uplifting the result to ten dimensions, we obtain solutions corresponding to various points of the N=2 moduli space. The more symmetric solution may correspond to a point with rotationally invariant classical vevs. By turning on seven-dimensional scalar fields, we find a solution corresponding to a linear distribution of vevs. Both solutions are conveniently studied with a D5-probe, which also confirms many of the standard expectations for N=2 solutions.
Dynamic universality class of large-N gauge theories
Natsuume, Makoto; Okamura, Takashi
In dynamic critical phenomena, singular behaviors appear not only in the order parameter but also in the other transport coefficients (due to the mode-mode coupling). However, this effect has not been observed in the AdS/CFT duality. We point out that this mode-mode coupling is suppressed by 1/N{sup 2} in the large-N gauge theories which correspond to model H in the classification of Hohenberg and Halperin. Thus, the effect cannot be seen in the classical supergravity approximation. We illustrate this point using the example of the N=4 super-Yang-Mills theory at a finite chemical potential. We also discuss the implications of this result to heavy-ion collisions.
Instanton calculus and loop operator in supersymmetric gauge theory
Kanno, Hiroaki; Moriyama, Sanefumi
We compute the one-point function of the glueball loop operator in the maximally confining phase of supersymmetric gauge theory using instanton calculus. In the maximally confining phase the residual symmetry is the diagonal U(1) subgroup and the localization formula implies that the chiral correlation functions are the sum of the contributions from each fixed point labeled by the Young diagram. The summation can be performed exactly by operator formalism of free fermions, which is also featured in the equivariant Gromov-Witten theory of P{sup 1}. By taking the Laplace transformation of the glueball loop operator, we find an exact agreement with the previous results for the generating function (resolvent) of the glueball one-point functions.
Investigations in gauge theories, topological solitons and string theories. Final report
Not Available
This is the Final Report on a supported research project on theoretical particle physics entitled ``Investigations in Gauge Theories, Topological Solitons and String Theories.`` The major theme of particle theory pursued has been within the rubric of the standard model, particularly on the interplay between symmetries and dynamics. Thus, the research has been carried out primarily in the context of gauge with or without chiral fermions and in effective chiral lagrangian field theories. The topics studied include the physical implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in a wide range of theories. A wide range of techniques of group theory, differential geometry and function theory have been applied to probe topological and conformal properties of quantum field theories in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD,the phenomenology of a possibly strongly interacting Higgs sector within the minimal standard model, and the relevance of solitonic ideas to non-perturbative phenomena at SSC energies.
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
CERN Winter School on Supergravity, Strings, and Gauge Theory 2010
The CERN Winter School on Supergravity, Strings, and Gauge Theory is the analytic continuation of the yearly training school of the former EC-RTN string network "Constituents, Fundamental Forces and Symmetries of the Universe". The 2010 edition of the school is supported and organized by the CERN Theory Divison, and will take place from Monday January 25 to Friday January 29, at CERN. As its predecessors, this school is meant primarily for training of doctoral students and young postdoctoral researchers in recent developments in theoretical high-energy physics and string theory. The programme of the school will consist of five series of pedagogical lectures, complemented by tutorial discussion sessions in the afternoons. Previous schools in this series were organized in 2005 at SISSA in Trieste, and in 2006, 2007, 2008, and 2009 at CERN, Geneva. Other similar schools have been organized in the past by the former related RTN network "The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions". This edition of the school is not funded by the European Union. The school is funded by the CERN Theory Division, and the Arnold Sommerfeld Center at Ludwig-Maximilians University of Munich. Scientific committee: M. Gaberdiel, D. Luest, A. Sevrin, J. Simon, K. Stelle, S. Theisen, A. Uranga, A. Van Proeyen, E. Verlinde Local organizers: A. Uranga, J. Walcher
Infrared singularities in Landau gauge Yang-Mills theory
Alkofer, Reinhard; Huber, Markus Q.; Schwenzer, Kai
We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Maas, Axel
Fixing a gauge in the nonperturbative domain of Yang-Mills theory is a nontrivial problem due to the presence of Gribov copies. In particular, there are different gauges in the nonperturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal Landau gauge and the absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, the finite-volume effects are also modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.
Noncommutative SO(2,3) gauge theory and noncommutative gravity
NASA Astrophysics Data System (ADS)
Dimitrijević, Marija; Radovanović, Voja
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3)⋆ group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action with the cosmological constant term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are of zeroth to fourth power in the curvature tensor and torsion. Trying to relate our results with f(R) and f(T) models, we analyze different limits of our model. In the limit of big cosmological constant and vanishing torsion we obtain an x-dependent correction to the cosmological constant; i.e. noncommutativity leads to an x-dependent cosmological constant. We also discuss the limit of small cosmological constant and vanishing torsion and the teleparallel limit.
Topological susceptibility near Tc in SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Xiong, Guang-Yi; Zhang, Jian-Bo; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping
Topological charge susceptibility χt for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χt with values decreasing from (188 (1) MeV) 4 to (67 (3) MeV) 4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4 /χt is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
Generalization of trinification to theories with 3N SU(3) gauge groups
Carone, Christopher D.
We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs.
Geometric Structure of the Translation Gauge Theory of Gravitation
NASA Astrophysics Data System (ADS)
Yoshida, H.
In the translation gauge theory of gravitation, we give a general expression of the affine connexion coefficient satisfying the following conditions: (i) It is a function of the vierbien b_kμ and of its first derivative bμk,ν. (ii) It is linear in bμk,ν. (iii) It satisfies the metricity condition. Our expression includes both of the connexion coefficients of the Riemann and Weitzenböck space-times as special ones, and hence, the space-time in the translation gauge theory is of Riemann-Cartan type. We fix the gravitational interaction of matter fields following Hayashi's method. The most general quadratic Lagrangian density of b_kμ is represented in terms of the curvature scalar and of the torsion tensor. In the case of electromagnetic field interacting with gravitational field, it is pointed out that the torsion tensor can give rise to observable effects if the field strength Fμν of the electromagnetic field is given by Fμν=nablaμAν-nablaνAμ. Besides the electric charge of the matter field there is a charge which is associated both with the gravitational and electromagnetic fields. In the case of the electromagnetic and gravitational fields produced by a spherically symmetric massive charged matter, the effects of the torsion tensor appear in the post-Newtonian term in the gravitational potential and in the ``post-Coulombian term'' in the electric field strength. We point out the available experimental data in the astronomy impose no restriction on the connexion coefficient.
Wilson loops in noncompact U(1) gauge theories at criticality
Metlitski, Max A.
We study the properties of Wilson loops in three-dimensional noncompact U(1) gauge theories with global Abelian symmetries. We use duality in the continuum and on the lattice to argue that, close to the critical point between the Higgs and Coulomb phases, all correlators of the Wilson loops are periodic functions of the Wilson loop charge, Q. The period depends on the global symmetry of the theory, which determines the magnetic flux carried by the dual particles. For single flavor scalar electrodynamics, the emergent period is Q=1. In the general case of N complex scalars with a U(1){sup N-1} global symmetry, the period is Q=N. We also give some arguments why this phenomenon does not generalize to theories with a full non-Abelian SU(N) symmetry, where no periodicity in Q is expected. Implications for lattice simulations, as well as for physical systems, such as easy-plane antiferromagnets and disordered superfluids, are noted.
Perturbative Quantum Gravity as a Double Copy of Gauge Theory and Implications for UV Properties
NASA Astrophysics Data System (ADS)
Bern, Zvi
The talk will review recent developments showing that in a precise sense gravity scattering amplitudes are double copies of corresponding gauge theory ones used to describe the strong subnuclear interactions. Underlying this is a correspondence between the color charges and kinematic numerators appearing in gauge theory scattering amplitudes. An application of these ideas will be given, demonstrating that within perturbation theory standard supergravity theories are much tamer in the ultraviolet than had been believed possible.
Model of the N-quark potential in SU(N) gauge theory using gauge-string duality
NASA Astrophysics Data System (ADS)
Andreev, Oleg
We use gauge-string duality to model the N-quark potential in pure Yang-Mills theories. For SU (3), the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the Δ-law at short distances and the Y-law at long distances.