Lattice formulation for 2d $ mathcal{N} $ = (2, 2), (4, 4) super Yang-Mills theories without admissibility conditions

摘要

A bstract We present a lattice formulation for two-dimensional $ mathcal{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, $ mathcal{N} $ = (8,8) supersymmetricYang-Mills theory and $ mathcal{N} $ = (2,2) supersymmetricQCD.