Dimensional reduction and the phase diagram of 5d Yang-Mills theory

TL;DR

This paper investigates the phase structure of 5d SU(2) Yang-Mills theory with a compact extra dimension using lattice simulations, revealing a scale hierarchy that allows for non-perturbative insights into effective 5d theories.

Contribution

It demonstrates the non-perturbative phase diagram of 5d Yang-Mills with a compact dimension and discusses the implications of scale separation for continuum limits.

Findings

Exponential scale separation between compactification and correlation length.

Full five-dimensional continuum limit is not achievable.

Potential for non-perturbative predictions of effective 5d theories.

Abstract

We present a non-perturbative study of the phase diagram of 5d SU(2) Yang-Mills theory with one compact extra dimension on the lattice. Assuming at least a modest scale separation between the cutoff and the compactification scales leads to an exponential separation between the compactification scale and the four-dimensional correlation length. While we demonstrate that it is not possible to take a full five-dimensional continuum limit, this dynamical generation of scale hierarchy opens up the possibility for us to make limited, but non-perturbative, predictions about continuum theories whose low-energy sector is described by an effective 5d Yang-Mills theory.