The supergravity dual of a theory with dynamical supersymmetry breaking

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.