Weyl fermions. The symmetry group generated by all these generators is known as the super-Poincaré group. In general there can be more than one set of supersymmetry generators, , which generate the corresponding supersymmetry, supersymmetry, and so on. Supersymmetry can also be constructed in other dimensions, most notably in (1+1) dimensions for its application in superstring theory. The Lagrangian of a supersymmetric theory must be invariant under the action of the super-Poincaré group. Examples of such theories include: Minimal Supersymmetric Standard Model (MSSM), supersymmetric Yang–Mills theory, and superstring theory. In a supersymmetric theory, every fermion has a bosonic superpartner and vice versa. If supersymmetry is promoted to a local symmetry, then the resultant gauge theory is an extension of general relativity called supergravity. Supersymmetry is a potential solution to many current problems in physics. For example, the hierarchy problem of the Standard Model—why the mass of the Higgs boson is not radiatively corrected (under renormalization) to a very high scale such as the grand unified scale or the Planck scale—can be resolved by relating the Higgs field and its super-partner, the Higgsino. Radiative corrections due to Higgs boson loops in Feynman diagrams are cancelled by corresponding Higgsino loops. Supersymmetry also offers answers to the grand unification of all gauge coupling constants in the Standard Model as well as the nature of dark matter. Nevertheless, , experiments have yet to provide evidence for the existence of supersymmetric particles. If supersymmetry were a true symmetry of nature, then it must be a broken symmetry, and the energy of symmetry breaking must be higher than those achievable by present-day experiments. Other spacetimes The theory, QED, QCD, as well as the whole Standard Model all assume a (3+1)-dimensional Minkowski space (3 spatial and 1 time dimensions) as the background on which the quantum fields are defined. However, QFT a priori imposes no restriction on the number of dimensions nor the geometry of spacetime. In condensed matter physics, QFT is used to describe (2+1)-dimensional electron gases. In high-energy physics, string theory is a type of (1+1)-dimensional QFT, while Kaluza–Klein theory uses gravity in extra dimensions to produce gauge theories in lower dimensions. In Minkowski space, the flat metric is used to raise and lower spacetime indices in the Lagrangian, e.g. where is the inverse of satisfying . For QFTs in curved spacetime on the other hand, a general metric (such as the Schwarzschild metric describing