From giant gravitons to black holes

TL;DR

This paper explores the connection between giant graviton configurations and black hole entropy in AdS spaces, providing a new saddle point analysis that matches dual black hole entropy in certain limits and extends to other dimensions.

Contribution

It introduces a saddle point analysis of giant graviton indices to compute black hole entropy at large N, including a novel approach to account for black holes of various sizes.

Findings

Large N entropy matches dual black hole entropy in the small black hole limit.

Giant graviton indices cancel due to gauge theory properties, allowing entropy calculation at general sizes.

Analytic continuation of SCFT free energies enables entropy computation for AdS4 and AdS7 black holes.

Abstract

We study AdS$_5$ black holes from a recently suggested giant graviton expansion formula for the index of $U(N)$ maximal super-Yang-Mills theory. We compute the large $N$ entropy at fixed charges and giant graviton numbers $n_I$ by a saddle point analysis, and further maximize it in $n_I$. This agrees with the dual black hole entropy in the small black hole limit. To get black holes at general sizes, one should note that various giant graviton indices cancel because gauge theory does not suffer from a Hagedorn-like pathology by an infinite baryonic tower. With one assumption on the mechanism of this cancellation, we account for the dual black hole entropy at general sizes. We interpret our results as analytic continuations of the large $N$ free energies of SCFTs, and based on it compute the entropies of AdS$_{4,7}$ black holes from M5, M2 giant gravitons.