Mean-Field Gauge Interactions in Five Dimensions I. The Torus

TL;DR

This paper investigates a five-dimensional SU(2) gauge theory on a lattice, identifying a phase transition and signs of dimensional reduction through mean-field analysis of fluctuations around a consistent background.

Contribution

It introduces a mean-field approach to analyze the phase structure and dimensional reduction in a five-dimensional lattice gauge theory with periodic boundary conditions.

Findings

Existence of a second order phase transition at finite gauge coupling.

Evidence for dimensional reduction in certain regimes.

Identification of a consistent mean-field background.

Abstract

We consider the lattice regularization of a five dimensional SU(2) gauge theory with periodic boundary conditions. We determine a consistent mean-field background and perform computations of various observables originating from fluctuations around this background. Our aim is to extract the properties of the system in regimes of its phase diagram where it seems to be in a dimensionally reduced state. Within the mean-field theory we establish the existence of a second order phase transition at finite value of the gauge coupling for anisotropy parameter less than one, where there is evidence for dimensional reduction.