Lattice gauge theories in the presence of a linear gauge-symmetry breaking

Abstract

We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP(1) model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge-invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP(1) gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case the behavior is extremely sensitive to GSB perturbations.

14 pages

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Cited by in corpus (11)

• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation
• Breaking of the gauge symmetry in lattice gauge theories
• Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields
• Multicomponent gauge-Higgs models with discrete Abelian gauge groups
• Gauge fixing and gauge correlations in noncompact Abelian gauge models
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields
• Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm