Supersymmetric Index Of Three-Dimensional Gauge Theory

TL;DR

This paper calculates the supersymmetric index of 3D N=1 super Yang-Mills theories with Chern-Simons interactions, revealing conditions for unbroken supersymmetry and implications for dynamical breaking.

Contribution

It provides a new computation method for the supersymmetric index in 3D gauge theories and clarifies the conditions under which supersymmetry remains unbroken.

Findings

Supersymmetry is unbroken if |k| ≥ h/2.

Dynamical supersymmetry breaking may occur if |k| < h/2.

Large |k| theories are massive and not fully characterized by standard criteria.

Abstract

In N=1 super Yang-Mills theory in three spacetime dimensions, with a simple gauge group $G$ and a Chern-Simons interaction of level $k$, the supersymmetric index $\Tr (-1)^F$ can be computed by making a relation to a pure Chern-Simons theory or microscopically by an explicit Born-Oppenheimer calculation on a two-torus. The result shows that supersymmetry is unbroken if $|k|\geq h/2$ (with $h$ the dual Coxeter number of $G$) and suggests that dynamical supersymmetry breaking occurs for $|k|<h/2$. The theories with large $|k|$ are massive gauge theories whose universality class is not fully described by the standard criteria.