The SCI of N $$ \mathcal{N} $$ = 4 USp(2N c ) and SO(N c ) SYM as a matrix integral

Abstract

Abstract We study the superconformal index of 4d N $$ \mathcal{N} $$ = 4 USp(2N c ) and SO(N c ) SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point solution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the USp(2N c ) case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with SU(N c ) gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.

Keywords

• Black Holes in String Theory
• Supersymmetric Gauge Theory
• AdS-CFT Correspondence
• Chern-Simons Theories