Lattice study of two-dimensional N = (2,2) super Yang-Mills theory at large N

We study two-dimensional N = (2, 2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte Carlo simulation for N 2; 3; 4; 5 and then extrapolate the result to N = infinity. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z(N))(2) symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.