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

TL;DR

This paper investigates the behavior of Wilson loops in three-dimensional non-compact U(1) gauge theories near criticality, revealing a periodic dependence on charge influenced by global symmetries, with implications for various physical systems.

Contribution

It demonstrates that Wilson loop correlators exhibit a charge periodicity determined by the global symmetry, a novel insight in the context of non-compact U(1) gauge theories at critical points.

Findings

Wilson loop correlators are periodic functions of charge near criticality.

The period depends on the global symmetry: Q=1 for single scalar flavor, Q=N for N scalars.

The phenomenon does not extend to non-abelian SU(N) symmetric theories.

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.