  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.
