The supergravity dual of a theory with dynamical supersymmetry breaking

TL;DR

This paper explores the supergravity dual of a little string theory with a focus on supersymmetry breaking, revealing a non-singular solution at the supersymmetry-preserving point and analyzing the effects of adding branes or anti-branes.

Contribution

It constructs a supergravity solution for the critical case of supersymmetry preservation and interprets the effects of brane additions on supersymmetry breaking.

Findings

A non-singular solution exists at the supersymmetry-preserving point k=N/2.

Adding branes preserves supersymmetry, while adding anti-branes breaks it.

The solution describes a confining phase at the critical point.

Abstract

We study the large $N$ limit of a little string theory that reduces in the IR to U(N) ${\cal N} =1$ supersymmetric Yang-Mills with Chern Simons coupling $k$. Witten has shown that this field theory preserves supersymmetry if $k\geq N/2$ and he conjectured that it breaks supersymmetry if $k< N/2$. We find a non-singular solution that describes the $k=N/2$ case, which is confining. We argue that increasing $k$ corresponds to adding branes to this solution, in a way that preserves supersymmetry, while decreasing $k$ corresponds to adding anti-branes, and therefore breaking supersymmetry.