Dimensional reduction from five-dimensional gauge theories

TL;DR

This paper investigates the phase structure of five-dimensional SU(2) gauge theories on anisotropic lattices, revealing phase transitions, dimensional reduction mechanisms, and decoupling phenomena through lattice simulations and various measurements.

Contribution

It provides new insights into phase transitions and dimensional reduction in five-dimensional gauge theories using lattice methods and anisotropic lattice configurations.

Findings

Identification of first and second order phase transitions.

Evidence of decoupling of hyperplanes orthogonal to the extra dimension.

Hints of dimensional reduction via compactification and anisotropic lattice spacing.

Abstract

We study the phase diagram of five-dimensional SU(2) gauge theories on anisotropic lattices with periodic boundary conditions. We locate a line of first order bulk phase transitions and second order phase transitions related to breaking of the center along one direction. A reduction to four dimensions occurs through compactification of one dimension but not only. By choosing a lattice spacing in the extra dimension larger than in the other dimensions, we find hints that the hyperplanes orthogonal to the extra dimension decouple from each other. Our analysis is based on measurements of Polyakov loops, the static potential extracted from Wilson loops and renormalized couplings defined through the static force and its derivative.