The Yang-Mills duals of small AdS black holes

TL;DR

This paper investigates the duality between small AdS black holes and certain saddle points in the large N matrix model of 4d N=4 Yang-Mills theory, revealing new thermodynamic instabilities.

Contribution

It analytically constructs saddle points corresponding to small black holes in the Yang-Mills matrix model, including novel thermodynamic instabilities.

Findings

Identification of saddle points dual to small black holes

Analytical construction of these saddle points

Discovery of thermodynamic instabilities in the model

Abstract

We study the large $N$ matrix model for the index of 4d $\mathcal{N}=4$ Yang-Mills theory and its truncations to understand the dual AdS$_5$ black holes. Numerical studies of the truncated models provide insights on the black hole physics, some of which we investigate analytically with the full Yang-Mills matrix model. In particular, we find many branches of saddle points which describe the known black hole solutions. We analytically construct the saddle points dual to the small black holes whose sizes are much smaller than the AdS radius. They include the asymptotically flat BMPV black holes embedded in large AdS with novel thermodynamic instabilities.