Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework

TL;DR

The paper argues that General Relativity in the AdS/CFT context, at least within the $1/2$-BPS sector, can be understood as a mean-field thermodynamical description of ultraviolet degrees of freedom. It develops a statistical foundation using Weyl-Wigner phase-space methods to map microstates of $N$ non-interacting fermions in the LLM sector to bulk geometries, showing that the classical limit yields phase-space droplets whose superposition underlies GR observables. Through a detailed analysis of the Superstar, it shows the natural microstate ensemble is non-equiprobable and corresponds to almost triangular Young diagrams, with the density operator embedded via the Groenewold construction yielding a consistent single-particle mixed-state picture. The work provides a coherent framework connecting microstate counting, phase-space coarse graining, and bulk GR observables, with implications for black-hole physics and extensions to bubbling AdS geometries in the $1/2$-BPS sector.

Abstract

In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.