The SCI of $$ \mathcal{N} $$ = 4 USp(2Nc) and SO(Nc) SYM as a matrix integral
Antonio Amariti, Marco Fazzi, Alessia Segati
Abstract
A bstract We study the superconformal index of 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 USp(2 N 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(2 N 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.