Two-dimensional compact N=(2,2) lattice super-Yang-Mills theory with exact supersymmetry

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 [F. Sugino, JHEP 0401 (2004) 015, hep-lat/0311021, F. Sugino, JHEP 0403 (2004) 067, hep-lat/0401017, F. Sugino, JHEP 0501 (2005) 016, hep-lat/0410035]. 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.