Note on the Witten index and the dynamical breaking of a supersymmetric gauge theory

Abstract

It is known that in order for a supersymmetric gauge theory to be dynamically broken a necessary but not sufficient condition is that the Witten index $(-1)^F=n_b^0-n_f^0$ is zero. In the case the Witten index is zero it is in general hard to distinguish between theories with or without dynamical supersymmetry breaking. In this work we show that for a large class of theories the cancellation of the Witten index by itself signals the formation of a quark condensate and therefore produces dynamical supersymmetry breaking.