Supersymmetry Breaking in Chern-Simons-matter Theories

TL;DR

This paper investigates the mechanisms of supersymmetry breaking in ${ m f N}=2$ Chern-Simons-matter theories by analyzing vacuum states and demonstrating supersymmetry breaking through non-zero vacuum energy in related models.

Contribution

It clarifies the supersymmetry breaking mechanism in ${ m f N}=2$ Chern-Simons-matter theories by studying related models with fundamental matter.

Findings

Supersymmetry breaking occurs when Chern-Simons level is below a critical value.

Vacuum energy is non-zero in models exhibiting supersymmetry breaking.

Analysis of related theories reveals the mechanism behind supersymmetry breaking.

Abstract

Some of supersymmetric Chern-Simons theories are known to exhibit supersymmetry breaking when the Chern-Simons level is less than a certain number. The mechanism of the supersymmetry breaking is, however, not clear from the field theory viewpoint. In this paper, we discuss vacuum states of ${\cal N}=2$ pure Chern-Simons theory and ${\cal N}=2$ Chern-Simons-matter theories of quiver type using related theories in which Chern-Simons terms are replaced with (anti-)fundamental chiral multiplets. In the latter theories, supersymmetry breaking can be shown to occur by examining that the vacuum energy is non-zero.