Disentangling the gravity dual of Yang-Mills theory

TL;DR

This paper demonstrates a method to reconstruct the gravity dual of a gauge theory from lattice data on entanglement entropy, providing insights into the holographic correspondence for pure glue Yang-Mills theory.

Contribution

It introduces a proof-of-concept for precision holography by reconstructing the dual gravity background from lattice entanglement entropy data in a three-dimensional SU(2) gauge theory.

Findings

Thermal entropy scales as T^{7/3} in the deconfining phase.

Entropy approaches the critical point smoothly, consistent with black hole thermodynamics.

Polyakov loop correlators provide insights into quark potential and Debye screening.

Abstract

A construction of a gravity dual to a physical gauge theory requires confronting data. We establish a proof-of-concept for precision holography, i.e., the explicit reconstruction of the dual background metric functions directly from the entanglement entropy (EE) of strip subregions that we extract from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on a three-dimensional Euclidean SU(2) theory in the deconfining phase. Holographic EE suggests, and we find evidence for, that the scaling of the thermal entropy with temperature is to power 7/3 and that it approaches smoothly the critical point, consistent with black hole thermodynamics. In addition, we provide frugal results on the potential between quenched quarks by the computation of the Polyakov loop correlators on the lattice. Holographic arguments pique curiosity in the substratum of Debye screening at strong coupling.