# Witten index and dynamical supersymmetry breaking of a gauge theory

## TL;DR

This paper estimates the Witten index in supersymmetric gauge theories, confirming known results for pure Yang Mills and showing zero index for theories with dynamical symmetry breaking, thus providing insights into supersymmetry breaking.

## Contribution

It offers a new calculation of the Witten index for complex supersymmetric gauge theories, aiding understanding of dynamical supersymmetry breaking.

## Key findings

- Witten index matches existing results for pure Yang Mills
- Witten index is zero for theories with dynamical symmetry breaking
- Provides new insights into supersymmetry breaking mechanisms

## 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.