Scaling Laws and Effective Dimension in Lattice SU(2) Yang-Mills Theory with a Compactified Extra Dimension

TL;DR

This study uses Monte Carlo simulations to explore how a compactified extra dimension affects the phase structure and effective dimensionality of a 5D SU(2) Yang-Mills lattice theory, revealing a transition from five to four dimensions as the radius decreases.

Contribution

It provides new insights into the scaling laws and effective dimension changes in lattice gauge theories with compactified extra dimensions, including the existence of a well-defined continuum limit.

Findings

Confining phase extends into weak coupling as R decreases.

Effective dimension transitions from five to four with decreasing R.

Existence of a continuum limit at fixed R/a_4 in both phases.

Abstract

Monte Carlo simulations are performed in a five-dimensional lattice SU(2) Yang-Mills theory with a compactified extra dimension, and scaling laws are studied. Our simulations indicate that as the compactification radius $R$ decreases, the confining phase spreads more and more to the weak coupling regime, and the effective dimension of the theory changes gradually from five to four. Our simulations also indicate that the limit $a_4 to 0$ with $R/a_4$ kept fixed exists both in the confining and deconfining phases if $R/a_4$ is small enough, where $a_4$ is the lattice spacing in the four-dimensional direction. We argue that the color degrees of freedom in QCD are confined only for $R < R_{\rm max}$, where a rough estimate shows that $1/R_{\rm max}$ lies in the TeV range. Comments on deconstructing extra dimensions are given.