Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality

Abstract

We study the properties of Wilson loops in three dimensional non-compact U(1) gauge theories with global abelian symmetries. We use duality in the continuum and on the lattice, to argue that close to the critical point between the Higgs and Coulomb phases, all correlators of the Wilson loops are periodic functions of the Wilson loop charge, Q. The period depends on the global symmetry of the theory, which determines the magnetic flux carried by the dual particles. For single flavour scalar electrodynamics, the emergent period is Q = 1. In the general case of N complex scalars with a U(1)^{N-1} global symmetry, the period is Q = N. We also give some arguments why this phenomenon does not generalize to theories with a full non-abelian SU(N) symmetry, where no periodicity in Q is expected. Implications for lattice simulations, as well as for physical systems, such as easy plane antiferromagnets and disordered superfluids, are noted.

25 pages, 1 figure

References in corpus (8)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The critical exponents of the superfluid transition in He4
• Putting competing orders in their place near the Mott transition
• Field- and temperature induced topological phase transitions in the three-dimensional $N$-component London superconductor
• Theory of quantum impurities in spin liquids
• Valence bond solid order near impurities in two-dimensional quantum antiferromagnets
• Critical properties of the N-color London model