Lattice Gauge Theory - Gravity duality and Coulomb's constant in five dimensions

TL;DR

This paper tests gauge theory-gravity duality in five dimensions by comparing a Coulomb-like constant derived from Wilson loops, using both gravitational and lattice methods, finding a 2% agreement.

Contribution

It introduces a new quantity, k5, for five-dimensional SU(N) gauge theories, and compares its value from gravity and lattice calculations to test duality.

Findings

2% numerical agreement between gravity and lattice results for k5

k5 is minimally sensitive to N, enabling comparison across methods

Validates gauge/gravity duality in a nonconformal, nonsupersymmetric setting

Abstract

The purpose of this paper is to perform a quantitative check of gauge theory - gravity duality in a nonconformal, nonsupersymmetric context. In order to do so we define k5, an object extracted from the Wilson Loop, that plays the role of Coulomb's constant for SU(N) gauge theories in five dimensions and we argue that one of its virtues is that it could be minimally sensitive to N. This allows us to compute k5 on one hand from the gravitational backreation of a large number N of D4-branes, and on the other from a lattice mean-field expansion for N=2. We find a 2% numerical agreement between the two approaches.