Witten index and dynamical supersymmetry breaking of a gauge theory

Abstract: We estimate the Witten index for a supersymmetric gauge theory with or without massless matter. For pure supersymmetric Yang Mills our result reproduces the results in the literature. For the known theories with dynamical symmetry breaking the Witten index is determined to be exactly zero. Our calculation sheds light on the possibility of dynamical supersymmetry breaking for those theories considered up to now unsolvable.