  We construct two-dimensional N=(2,2) lattice super Yang-Mills theory, where
the gauge and Higgs fields are all represented by U(N) compact variables, with
keeping one exact supercharge along the line of the papers [1,2,3].
Interestingly, requirements of the exact supersymmetry as well as of the
compact gauge and Higgs fields lead to the gauge group U(N) rather than SU(N).
As a result of the perturbative renormalization argument, the model is shown to
flow to the target continuum theory without any fine-tuning. Different from the
case of noncompact Higgs fields, the path integral along the flat directions is
well-defined in this model.
