In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning quarks at all. It is a nonlinear sigma model with the principal homogeneous space of the Lie group SU(N) as its target manifold, where N is the number of quark flavors. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer–Cartan form of SU(N). The internal global symmetry of this model is SU(N)L × SU(N)R, the left and right copies, respectively; where the left copy acts as the left action upon the target space, and the right copy acts as the right action. The left copy represents flavor rotations among the left-handed quarks, while the right copy describes rotations among the right-handed quarks, while these, L and R, are completely independent of each other. The axial pieces of these symmetries are spontaneously broken so that the corresponding scalar fields are the requisite Nambu−Goldstone bosons. This model admits topological solitons called skyrmions. Departures from exact chiral symmetry are dealt with in chiral perturbation theory. An outline of the original, 2-flavor model The chiral model of Gürsey (1960; also see Gell-Mann and Lévy) is now appreciated to be an effective theory of QCD with two light quarks, u, and d. The QCD Lagrangian is approximately invariant under independent global flavor rotations of the left- and right-handed quark fields, where τ denote the Pauli matrices in the flavor space and θL, θR are the corresponding rotation angles. The corresponding symmetry group is the chiral group, controlled by the six conserved currents which can equally well be expressed in terms of the vector and axial-vector currents The corresponding conserved charges generate the algebra of the chiral group, with I=L,R, or, equivalently, Application of these commutation relations to hadronic reactions dominated current algebra calculations in the early seventies of the last century. At the level of hadrons, pseudoscalar mesons, the ambit of the chiral model, the chiral group is spontaneously broken down to , by the QCD vacuum. That is, it is realized nonlinearly, in the Nambu–Goldstone mode: The QV annihilate the vacuum, but the QA do not! This is visualized nicely through a geometrical argument based on the fact that the Lie algebra of