The Superconformal Index and Black Hole Instabilities

TL;DR

This paper investigates the superconformal index of ${ m extbf{N}=4}$ supersymmetric Yang-Mills theory, revealing deviations from black hole entropy at small $N$, and introduces a giant graviton expansion method to explore supersymmetric phases and configurations.

Contribution

It introduces a giant graviton expansion approach for the superconformal index, enabling explicit calculations at small $N$ and revealing new phases beyond traditional black hole solutions.

Findings

Deviations from black hole entropy observed at small $N$.

Giant graviton expansion efficiently computes the index with up to two gravitons.

Field theory index encodes information about diverse supersymmetric phases.

Abstract

The superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with gauge group $\mathrm{U}(N)$ has provided powerful insights into the entropy of supersymmetric black holes in AdS$_5\times S^5$, including some sub-leading logarithmic and non-perturbative corrections. Recently, the phase space of supersymmetric solutions has been argued to contain configurations other than the asymptotically AdS$_5$ black hole. Such configurations include the so-called grey galaxies where the black hole at the center is surrounded by a gas of gravitons. By numerically evaluating the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills at small values of $N$, we detect systematic deviations from the entropy of black holes with two distinct angular momenta. We find that the giant graviton expansion of the index is a numerically efficient way of evaluating the index that complements the direct character evaluation and allows for explicit access to $N\le 15$ with up to two giant gravitons in the expansion. We find it remarkable that a supersymmetric quantity in field theory, usually thought of as a rigid counting observable, indeed contains information about different phases in the space of supersymmetric solutions on the gravity side.