Three-dimensional Abelian and non-Abelian gauge Higgs theories

Abstract

Gauge symmetries and Higgs mechanisms are key features of theories describing high-energy particle physics and collective phenomena in statistical and condensed-matter physics. In this review we address the collective behavior of systems of multicomponent scalar fields interacting with gauge fields, which can be already present in the underlying microscopic system or emerge only at criticality. The interplay between local gauge and global symmetries determines the phase diagram, the nature of the Higgs phases, and the nature of phase transitions between the high-temperature disordered and the low-temperature Higgs phases. However, additional crucial features determine the universal properties of the critical behavior at continuous transitions. Specifically, their nature also depends on the role played by the gauge modes at criticality. Effective (Abelian or non-Abelian) gauge Higgs field theories emerge when gauge modes develop critical correlations. On the other hand, a more standard critical behavior, which admits an effective description in terms of Landau-Ginzburg-Wilson ${\Phi }^4$ theories, occurs when gauge-field modes are short ranged at the transition. In the latter case, gauge fields only prevent non-gauge invariant correlation functions from becoming critical. This review covers the recent progress made in the study of Higgs systems with Abelian and non-Abelian gauge fields. We discuss the equilibrium thermodynamic properties of systems with a classical partition function, focusing mainly on three-dimensional systems, and only briefly discussing two-dimensional models. However, by using the quantum-to-classical mapping, the results on the critical behavior for classical systems in $D=d+1$ dimensions can be extended to quantum transitions in $d$ dimensions.

117 pages, 50 pdf figures. References and comments added. Accepted for publication by Physics Reports

References in corpus (108)

• The electronic properties of graphene
• Many-Body Physics with Ultracold Gases
• Probing many-body dynamics on a 51-atom quantum simulator
• Generalized Global Symmetries
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Generalized Symmetries in Condensed Matter
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Algebraic spin liquid as the mother of many competing orders
• The critical exponents of the superfluid transition in He4
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Robustness of a perturbed topological phase
• Critical Behavior of a Trapped Interacting Bose Gas
• Phase transitions in the early and the present Universe
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• The critical behavior of three-dimensional Ising spin glass models
• Monte Carlo study of an improved clock model in three dimensions
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Theory of the nodal nematic quantum phase transition in superconductors
• Coherent and dissipative dynamics at quantum phase transitions
• On the Phase Structure of Many-Flavor QED${}_3$
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• On the Ambiguity of Spontaneously Broken Gauge Symmetry
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Coulomb gas transitions in three-dimensional classical dimer models
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Diagnosing Deconfinement and Topological Order
• Finite-size scaling at first-order quantum transitions
• Gauge theory picture of an ordering transition in a dimer model
• First-order electroweak phase transitions: a nonperturbative update
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Emergent ${\mathbb{Z}}_2$ gauge theories and topological excitations in Rydberg atom arrays
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Fixed point stability and decay of correlations
• Lattice Abelian-Higgs model with noncompact gauge fields
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• New Developments in the Numerical Conformal Bootstrap
• The critical behavior of 3D Ising glass models: universality and scaling corrections
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Critical properties of the N-color London model
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Numerical study of duality and universality in a frozen superconductor
• Three-dimensional antiferromagnetic CP(N-1) models
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Multicritical point of the three-dimensional Z_2 gauge Higgs model
• Percolation of Vortices in the 3D Abelian Lattice Higgs Model
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Nodal quasiparticles and the onset of spin density wave order in the cuprates
• Stripe melting and quantum criticality in correlated metals
• Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Ideal topological gas in the high temperature phase of SU(3) gauge theory
• Cubic fixed point in three dimensions: Monte Carlo simulations of the ${\varphi }^4$ model on the lattice
• Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Lattice gauge theories in the presence of a linear gauge-symmetry breaking
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
• Bootstrapping traceless symmetric $O(N)$ scalars
• Spin-density-wave order in cuprates
• Landau-Ginzburg-Wilson approach to critical phenomena in the presence of gauge symmetries
• Comparative study of Higgs transition in one-component and two-component lattice superconductor models
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries
• 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
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Effective field theory for Sp(N) antiferromagnets and its phase structure
• Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials
• Disordered Ising model with correlated frustration
• Chiral symmetry breaking and monopole dynamics in non-compact QED3 coupled to a four-fermi interaction
• Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories
• Two-dimensional multicomponent Abelian-Higgs lattice models
• Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition
• Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields
• Gauge fixing and gauge correlations in noncompact Abelian gauge models
• Multicomponent gauge-Higgs models with discrete Abelian gauge groups
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors
• Confinement-Higgs and deconfinement-Higgs transitions in three-dimensional $Z(2)$ LGT
• Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models
• Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry
• Exploring the 3D Ising gauge-Higgs model in exact Coulomb gauge and with a gauge-invariant substitute for Landau gauge

Cited by in corpus (7)

• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Revisiting vestigial order in nematic superconductors: gauge-field mechanisms and model constraints
• Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models