Holographic Tests for Giant Graviton Expansion

TL;DR

This paper explores the giant graviton expansion of the superconformal index to analyze dual $AdS_5$ black holes, revealing stability conditions, black hole microstate interpretations, and extensions to defect insertions and various holographic backgrounds.

Contribution

It introduces a saddle point analysis of the giant graviton index for $AdS_5$ black holes, identifying stability regimes and extending the framework to include defects and different dual geometries.

Findings

Identified a regime of fugacities ensuring black hole stability.

Connected small black holes to brane bound states via the expansion.

Extended analysis to include surface defects and other holographic backgrounds.

Abstract

It has been proposed that the superconformal index admits a novel reformulation, called giant graviton expansion. In this paper, we investigate the properties of dual $AdS_5$ black holes using the giant graviton expansion framework. First, we compute the entropy of black holes in $AdS_5\times S^5$ with fixed charges through a large $N$ saddle point analysis on the giant graviton index and further extremize it in the wrapping number. We identify a specific regime of fugacities where our saddle point analysis is valid. It turns out that this condition ensures the absence of closed-time-like curves and the stability of dual black hole solutions with equal charges. In addition, the giant graviton expansion of the index provides insights into how small black holes in AdS can be interpreted as bound states of branes. We extend our study to include the giant graviton expansion with the insertion of a half-BPS surface defect in $\mathcal{N}=4$ SYM with a $U(N)$ gauge group. Finally, we test the giant graviton expansion in various holographic theories whose dual geometries are $AdS_5\times S^5/\mathbb{Z}_k$ and $AdS_5\times SE_5$.