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.
Highlights
Introduction.—Gauge symmetries play a key role in the construction of the theoretical models of fundamental interactions [1,2] and in the description of emergent phenomena in condensed-matter and statistical physics [3,4,5,6,7,8]
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 address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from UðNÞ to Oð2NÞ, which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass
Summary
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 SUðNÞ 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 study the role of GSB perturbations at the critical transitions of gauge-invariant models, to understand whether and when they are relevant, i.e., they break gauge invariance in the low-energy or large-distance behavior (continuum limit). If this is the case, GSB terms may lead to different continuum limits, as we shall see.
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