Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories

TL;DR

This paper demonstrates that supersymmetry can be spontaneously broken in certain three-dimensional gauge theories, using brane configurations in string theory to analyze the conditions and mechanisms of breaking.

Contribution

It provides a novel string theory-based analysis of supersymmetry breaking in 3D gauge theories, including explicit conditions for breaking in various supersymmetric models.

Findings

Supersymmetry is broken in N=3 SU(n) Chern-Simons theories when n>|k|.

Supersymmetry breaking occurs in N=2 and N=1 deformations under similar conditions.

Instanton effects induce supersymmetry breaking in certain N=1 mass-deformed theories.

Abstract

It is shown that supersymmetry is spontaneously broken in certain three-dimensional supersymmetric gauge theories, by using the s-rule in their string theory realization as brane configurations. In particular, supersymmetry is broken in N=3 supersymmetric Yang-Mills-Chern-Simons theory with gauge group SU(n) and CS coefficient k, as well as in its N=2 and N=1 deformations, when n>|k|. In addition, supersymmetry is broken in the N=1 mass deformation of N=2 supersymmetric Yang-Mills theory with gauge group SU(n) and one matter multiplet when n>1. In the latter case the breaking is induced by an instanton-generated repulsive potential.