Global symmetry breaking in gauge theories: the case of multiflavor scalar chromodynamics

TL;DR

This paper examines the role of gauge fields in phase transitions of gauge theories by numerically studying three-dimensional scalar lattice models with non-abelian symmetries, challenging the assumption that gauge fields are irrelevant.

Contribution

It provides a numerical investigation into the validity of ignoring gauge fields in effective critical models of gauge theories with global symmetry breaking.

Findings

Gauge fields can influence critical behavior in gauge theories.

Numerical results clarify when gauge fields are relevant or irrelevant.

Critical exponents are computed with high accuracy for these models.

Abstract

Universal features of continuous phase transitions can be investigated by studying the $\phi^4$ field theory with the corresponding global symmetry breaking pattern. When gauge symmetries are present, the same technique is usually applied to a gauge-invariant order parameter field, as in the Pisarski-Wilczek analysis of the QCD chiral phase transition. Gauge fields are thus assumed to be irrelevant in the effective critical model, a fact that is however far from trivial. We will investigate the validity of this approach using three-dimensional scalar lattice models with non-abelian global and local symmetries, for which critical exponents and scaling functions can be numerically determined with high accuracy.