The SUSY Index Beyond the Cardy Limit

TL;DR

This paper investigates the superconformal index of 4d $ ext{SU}(N)$ super Yang-Mills theory, revealing dominant contributions at large $N$ that correspond to black hole saddles and showing the potential for 1-loop exactness in the gravitational perturbative series.

Contribution

It introduces a Bethe Ansatz approach to analyze the superconformal index, computing subleading terms and suggesting the 1-loop exactness of the gravitational series around black hole saddles.

Findings

Leading order reproduces supersymmetric black hole saddles.

No $1/N$ corrections beyond the computed terms.

Potential 1-loop exactness of the gravitational series.

Abstract

We analyze a set of contributions to the superconformal index of 4d $\mathcal{N} = 4$ $SU(N)$ super Yang-Mills using the Bethe Ansatz approach. These contributions dominate at the large $N$ limit, where their leading order in $N$ reproduces various supersymmetric Euclidean black hole saddles in the dual theory, and they also dominate for finite $N$ in high temperature Cardy-like limits. We compute the $O(N^0)$ terms, including those exponentially suppressed in the Cardy limit, and show that there are no $1/N$ corrections beyond them. Under certain assumptions, it implies that the gravitational perturbative series around these black hole saddles is 1-loop exact.