On the large N limit of SU(N) lattice gauge theories in five dimensions

TL;DR

This paper develops tools to analyze fluctuations in five-dimensional SU(N) lattice gauge theories, computes a Coulomb-like constant, and shows its N-independence in the large N limit, with a notable deviation from holographic predictions.

Contribution

It introduces methods for fluctuation analysis and computes a key observable in 5D SU(N) gauge theories, revealing large N behavior and deviations from holographic models.

Findings

The Coulomb constant k5 becomes N-independent at large N.

Numerical value of k5 deviates by 17% from holographic predictions.

Tools for fluctuation computations around mean-field backgrounds are established.

Abstract

We develop the necessary tools for computing fluctuations around a mean-field background in the context of SU(N) lattice gauge theories in five dimensions. In particular, expressions for the scalar observable and the Wilson Loop are given. As an application, using these observables we compute a certain quantity k5 that can be viewed as Coulomb's constant in five dimensions. We show that this quantity becomes independent of N in the large N limit. Furthermore, the numerical value of k5 we find for SU(infinity) deviates by 17% from its value predicted by holography.