Supersymmetry Breaking Phase in Three Dimensional Large N Gauge Theories

TL;DR

This paper investigates the supersymmetry breaking phase in three-dimensional large N gauge theories with massive matter, using localization on the ellipsoid to identify a confining phase characterized by a vanishing Polyakov loop.

Contribution

It introduces a large N saddle point solution for supersymmetric gauge theories on the ellipsoid, revealing a confining phase with SUSY breaking in the flat space limit.

Findings

Large N saddle point solution found for gauge theories with massive matter.

The solution indicates a confining phase with vanishing Polyakov loop.

SUSY is spontaneously broken in the gapped phase at large N.

Abstract

Three dimensional supersymmetric gauge theories are often in a gapped phase, in which SUSY is spontaneously broken, if all the matter fields are massive and decoupled in the low energy. We study this phase in the large $N$ limit using the localization technique for the theory on the ellipsoid, which interpolates the round three sphere and the flat space compactified on $S^1$. We find a large $N$ saddle point solution for the gauge theory with some massive matter fields. This solution gives a vanishing (generalized) Polyakov loop in the flat space limit, thus, it corresponds to the confining phase at the leading order in the $1/N$ expansion.