Supersymmetric Index and s-rule for Type IIB Branes

TL;DR

This paper explores the supersymmetric index of certain SU(n) gauge theories using Type IIB brane configurations, revealing conditions for supersymmetry breaking and constructing theories with identical indices.

Contribution

It introduces a brane-based method to compute the supersymmetric index and explains supersymmetry breaking via the s-rule, also constructing families of theories with the same index.

Findings

Supersymmetry breaks when k<n, explained by the s-rule.

The supersymmetric index equals the count of supersymmetric brane configurations.

Constructed a family of theories sharing the same supersymmetric index.

Abstract

We investigate the supersymmetric index of N=2,3 SU(n) supersymmetric Yang-Mills Chern Simons theories at level k by using the brane configuration with a (p,q)5-brane. We can explain that the supersymmetry breaking occurs when k<n in terms of the s-rule for Type IIB branes. The supersymmetric index coincides with the number of the possible supersymmetric brane configurations. We also discuss a construction of a family of theories which have the same supersymmetric index.