Testing Dimensional Reduction in SU(2) Gauge Theory

TL;DR

This paper evaluates the accuracy of dimensional reduction in SU(2) gauge theory at high temperatures by comparing perturbative effective couplings with lattice results, noting increasing discrepancies as temperature decreases.

Contribution

It provides a numerical assessment of dimensional reduction's validity in SU(2) gauge theory across a range of temperatures, highlighting potential implementation differences.

Findings

Discrepancies grow as temperature approaches T_c

Perturbative and lattice results diverge below 4 T_c

Implementation differences may influence results

Abstract

At high temperature, every $(d+1)$-dimensional theory can be reformulated as an effective theory in $d$ dimensions. We test the numerical accuracy of this Dimensional Reduction for (3+1)-dimensional SU(2) by comparing perturbatively determined effective couplings with lattice results as the temperature is progressively lowered. We observe an increasing disagreement between numerical and perturbative values from $T=4 T_c$ downwards, which may however be due to somewhat different implementations of dimensional reduction in the two cases.