Breaking of the gauge symmetry in lattice gauge theories

TL;DR

This paper investigates how gauge-symmetry breaking perturbations affect the critical behavior of lattice gauge theories, focusing on the Abelian-Higgs model and revealing an effective symmetry enlargement and unique renormalization-group flow.

Contribution

It provides a detailed analysis of the impact of gauge-symmetry breaking terms on the critical properties and phase transitions in lattice gauge theories, highlighting symmetry changes and RG flow.

Findings

Gauge-symmetry breaking perturbations alter critical behavior.

An effective symmetry enlargement from U(N) to O(2N) occurs.

A cyclic renormalization-group flow is identified.

Abstract

We study perturbations that break gauge symmetries in lattice gauge theories. As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH) model with an N-component scalar field and a noncompact gauge field, which is invariant under U(1) gauge and SU(N) transformations. We consider gauge-symmetry breaking perturbations that are quadratic in the gauge field, such as a photon mass term, and determine their effect on the critical behavior of the gauge-invariant model, focusing mainly on the continuous transitions associated with the charged fixed point of the AH field theory. We discuss their relevance and compute the (gauge-dependent) exponents that parametrize the departure from the critical behavior (continuum limit) of the gauge-invariant model. We also address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass.