Supersymmetric index and s-rule for type IIB branes

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, g)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.