The Stefan-Boltzmann law: SU(2) versus SO(3) lattice gauge theory

TL;DR

This paper compares SU(2) and SO(3) lattice gauge theories at high temperatures, focusing on their Stefan-Boltzmann constants, revealing differences in how closely they approach continuum values and questioning their equivalence in the continuum limit.

Contribution

It provides a comparative analysis of SU(2) and SO(3) lattice gauge theories' thermodynamic limits, highlighting differences in their approach to continuum physics.

Findings

SU(2) lattice results underestimate the continuum Stefan-Boltzmann constant.

SO(3) lattice results are closer to the continuum value.

The study raises questions about the equivalence of SU(2) and SO(3) in the continuum limit.

Abstract

We investigate the high temperature limit of SU(2) and SO(3) lattice gauge theory, respectively. In particular, we study the Stefan-Boltzmann constant in both cases. As is well known, the Stefan-Boltzmann constant extracted from SU(2) lattice gauge theory by incorporating finite size effects is smaller than the continuum value which assumes three gluon degrees of freedom. On the other hand, the extrapolation of our SO(3) lattice data comes much closer to the continuum value. This rises the question whether SU(2) and SO(3) lattice gauge theories represent different quantum theories in the continuum limit.