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

Abstract

Abstract We study the superconformal index of 4d $$ \mathcal{N} $$ N = 4 USp(2Nc) and SO(Nc) 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(2Nc) case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with SU(Nc) gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.