Breaking the gauge symmetry in lattice gauge-invariant models

TL;DR

This paper investigates how gauge symmetry breaking terms affect the continuum limit of three-dimensional gauge theories, showing that gauge symmetry remains stable unless gauge fields are critical at the transition.

Contribution

It provides a detailed analysis of the conditions under which gauge symmetry is destabilized by symmetry-breaking perturbations in lattice gauge-invariant models.

Findings

Gauge symmetry is robust when gauge fields are not critical.

Gauge symmetry is lost at charged critical transitions when symmetry-breaking terms are added.

The study clarifies the stability of gauge symmetry in different critical regimes.

Abstract

We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a U(1) gauge field. We discuss under which conditions a gauge-symmetry breaking term destabilizes the critical behavior (continuum limit) of the gauge-invariant theory. We find that the gauge symmetry is robust at transitions at which gauge fields are not critical. At charged transitions, where gauge fields are critical, gauge symmetry is lost as soon as the perturbation is added.