5d Black Hole as Emergent Geometry of Weakly Interacting 4d Hot Yang-Mills Gas

TL;DR

This paper shows that a five-dimensional anti-de Sitter black hole geometry naturally emerges as the holographic dual of a weakly interacting four-dimensional N=4 superconformal Yang-Mills theory, using instanton moduli space and information geometry.

Contribution

It introduces a novel approach to derive the dual geometry from instanton moduli space using Fisher-Rao information metric, applicable at weak coupling and small gauge group rank.

Findings

Moduli space metric is asymptotically anti-de Sitter.

Horizon appears at a radial distance related to temperature.

Lorentzian signature reveals a singularity at the origin.

Abstract

We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N=4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao "information geometry". In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak `t Hooft coupling.