Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions

Abstract

We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge groups are considered, gauge fields are expressed by unitary link variables, and one or two supercharges are preserved on the two-dimensional square lattice. There does not appear fermion doubler, and no fine-tuning is required to obtain the desired continuum theories in a perturbative argument. This formulation is expected to serve as a more convenient basis for numerical simulations. The same approach will also be useful to other two-dimensional supersymmetric lattice gauge theories with unitary link variables constructed so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2) supersymmetric QCD.