Duality and scaling in 3-dimensional scalar electrodynamics

Abstract

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for the scaling exponents of the gauge theory transition in the type II region, and allows thus to be scrutinized empirically. We review these predictions, and carry out numerical lattice Monte Carlo measurements to test them: a number of exponents, characterising the two phases as well as the transition point, are found to agree with expectations, supporting the conjecture. We explain why some others, like the exponent characterising the photon correlation length, appear to disagree with expectations, unless very large system sizes and the extreme vicinity of the transition point are considered. Finally, we remark that in the type I region the duality implies an interesting quantitative relationship between a magnetic flux tube and a 2-dimensional non-topological soliton.

27 pages. v2: reference and minor clarifications added, to appear in Nucl.Phys.B

References in corpus (36)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Critical Exponents of the N-vector model
• Critical behavior of the three-dimensional XY universality class
• 3D Physics and the Electroweak Phase Transition: Perturbation Theory
• Critical fluctuations in superconductors and the magnetic field penetration depth
• High precision Monte Carlo study of the 3D XY-universality class
• Phase Diagram of Superconductors from Non-Perturbative Flow Equations
• Topological phase-fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors
• Dual superconductor models of color confinement
• The order of the metal to superconductor transition
• Lattice-continuum relations for 3d SU(N)+Higgs theories
• Anomalous scaling dimensions and stable charged fixed-point of type-II superconductors
• Masses and Phase Structure in the Ginzburg-Landau Model
• Critical Behavior of the Meissner Transition in the Lattice London Superconductor
• O(a) errors in 3-D SU(N) Higgs theories
• Dual description of the superconducting phase transition
• On the Possibility of Second-Order Phase Transitions in Spontaneously Broken Gauge Theories
• Three-dimensional U(1) gauge+Higgs theory as an effective theory for finite temperature phase transitions
• Continuum dual theory of the transition in 3D lattice superconductor
• Numerical study of duality and universality in a frozen superconductor
• Vortex tension as an order parameter in three-dimensional U(1)+Higgs theory
• Q-ball dynamics from atomic Bose-Einstein condensates
• The monopole mass in the three-dimensional Georgi-Glashow model
• Topological defects in lattice gauge theories
• Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter $\kappa$
• A Candidate for Exact Continuum Dual Theory for Scalar QED${}_3$
• Statistical mechanics of vortices from field theory
• Numerical studies of the phase diagram of layered type II superconductors in a magnetic field
• Magnetic permeability of near-critical 3d abelian Higgs model and duality
• Superflow-Stabilized Nonlinear NMR in Rotating 3He-B
• The 3d Effective Field Theory for Finite Temperature Scalar Electrodynamics
• Electromagnetic Self-Duality in a Lattice Model
• Critical behaviour of the Ginzburg-Landau model in the type II region

Cited by in corpus (14)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Duality between $(2+1)d$ Quantum Critical Points
• Field- and temperature induced topological phase transitions in the three-dimensional $N$-component London superconductor
• Phase transitions in a three dimensional $U(1)\times U(1)$ lattice London superconductor: Metallic superfluid and charge-4e superconducting states
• Gauge theory picture of an ordering transition in a dimer model
• Valence bond solid order near impurities in two-dimensional quantum antiferromagnets
• Mass of a quantum 't Hooft-Polyakov monopole
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Constraints of kinematic bosonization in two and higher dimensions
• Evidence for 3d bosonization from monopole operators
• AdS from CFT for scalar QED
• Magnetic field induced 3D to 1D crossover in type II superconductors
• Charged and neutral fixed points in the O(N)+O(N)-model with Abelian gauge fields
• Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality