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

## TL;DR

This paper explores how the vanishing of the Witten index in certain supersymmetric gauge theories indicates the formation of a quark condensate, leading to dynamical supersymmetry breaking.

## Contribution

It demonstrates that for a broad class of theories, the cancellation of the Witten index directly signals dynamical supersymmetry breaking via quark condensate formation.

## Key findings

- Witten index zero correlates with quark condensate formation
- Cancellation of the Witten index indicates dynamical SUSY breaking
- Provides criteria for identifying SUSY breaking in gauge theories

## 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.