Exact QFT duals of AdS black holes

TL;DR

This paper constructs exact large N saddle points of the matrix model for the $ ext{AdS}_5$ black hole duals in $ ext{AdS}_5 imes S^5$, revealing new eigenvalue distributions and connections to Bethe ansatz equations.

Contribution

It introduces novel eigenvalue solutions for the matrix model of $ ext{AdS}_5$ black holes, including areal distributions and multi-cut saddle points, and links saddle point equations to Bethe ansatz.

Findings

Linear eigenvalue distributions for collinear chemical potentials

Areal eigenvalue distributions for non-collinear chemical potentials

Emergence of Bethe ansatz equations from saddle point analysis

Abstract

We construct large $N$ saddle points of the matrix model for the $\mathcal{N}=4$ Yang-Mills index dual to the BPS black holes in $AdS_5\times S^5$, in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large $N$ saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.