Lattice formulation of two-dimensional N=(2,2) SQCD with exact supersymmetry

We construct a lattice model for two-dimensional N=(2,2) supersymmetric QCD (SQCD), with the matter multiplets belonging to the fundamental or anti-fundamental representation of the gauge group U(N) or SU(N). The construction is based on the topological field theory (twisted supercharge) formulation and exactly preserves one supercharge along the line of the papers [F. Sugino, JHEP 0401 (2004) 015; F. Sugino, JHEP 0403 (2004) 067; F. Sugino, JHEP 0501 (2005) 016; F. Sugino, Phys. Lett. B 635 (2006) 218] for pure supersymmetric Yang-Mills theories. In order to avoid the species doublers of the matter multiplets, we introduce the Wilson terms and the model is defined for the case of the number of the fundamental matters (n+) equal to that of the anti-fundamental matters (n−). If some of the matter multiplets decouple from the theory by sending the corresponding anti-holomorphic twisted masses to the infinity, we can analyze the general n+≠n− case, although the lattice model is defined for n+=n−. By computing the anomaly of the U(1)A R-symmetry in the lattice perturbation, we see that the decoupling is achieved and the anomaly for n+≠n− is correctly obtained.