The superconformal index of $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM as a matrix integral
Abstract
We study the superconformal index of 4d and 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 case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.
Keywords
Cite
@article{arxiv.2012.15208,
title = {The superconformal index of $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM as a matrix integral},
author = {Antonio Amariti and Marco Fazzi and Alessia Segati},
journal= {arXiv preprint arXiv:2012.15208},
year = {2021}
}
Comments
29 pages, 1 appendix; v2: typos corrected and references added; v3: corrected a mistake in the appendix, expanded discussion about logarithmic corrections in the introduction and about saddle points for SO groups in section 4