Dimensional reduction and confinement from five dimensions

TL;DR

This paper investigates five-dimensional SU(2) gauge theories using lattice mean-field methods, demonstrating a continuum limit with decoupled four-dimensional hyperplanes and signs of confinement, supported by Monte Carlo simulations.

Contribution

It introduces a non-perturbative lattice approach to study dimensional reduction and confinement in five-dimensional gauge theories, highlighting the role of anisotropy.

Findings

Continuum limit with decoupled hyperplanes

Signs of confinement in static potential

Phase diagram insights from Monte Carlo simulations

Abstract

We study non-perturbatively five-dimensional SU(2) gauge theories by means of the mean-field expansion on the lattice. On the anisotropic torus we show that a continuum limit can be defined where the anisotropy is a relevant parameter. The analysis of the static force supports the fact that the four-dimensional hyperplanes decouple from each other in the continuum limit. Clear signs of confinement are found in the static potential along the hyperplanes. We present first results from Monte Carlo simulations on the phase diagram.