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.

arXiv comment14 pages

References in corpus (39)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• Quantum Field Theory in the Large N Limit: a review
• Simulating Lattice Gauge Theories within Quantum Technologies
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• The critical exponents of the superfluid transition in He4
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Review on novel methods for lattice gauge theories
• Carving out OPE space and precise $O(2)$ model critical exponents
• Finite size effects on measures of critical exponents in d=3 O(N) models
• N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Monte Carlo study of an improved clock model in three dimensions
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Gauge theory for the cuprates near optimal doping
• Surface and bulk transitions in three-dimensional O(n) models
• Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Quantum simulation of $(1+1)$-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases
• Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Four-point renormalized coupling constant in O(N) models
• Atomic Quantum Simulation of Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry
• Lattice Abelian-Higgs model with noncompact gauge fields
• Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator
• CP^1+U(1) Lattice Gauge Theory in Three Dimensions: Phase Structure, Spins, Gauge Bosons, and Instantons
• Multicomponent compact Abelian-Higgs lattice models
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• O(N) and RP^{N-1} Models in Two Dimensions
• Gauge symmetry from decoupling
• Three-dimensional ferromagnetic CP(N-1) models
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Deconfinement of Spinons on Critical Points: Multi-Flavor CP${}^1$ + U(1) Lattice Gauge Theory in Three Dimensions
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Large-N behavior of three-dimensional lattice CP(N-1) models
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories

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