The Abelian Higgs Model as an Ensemble of Vortex Loops

TL;DR

This paper models vortex dipoles and loops in the Abelian Higgs model as a grand canonical ensemble, deriving effective theories and showing their equivalence to compact QED with screening effects in the London limit.

Contribution

It introduces a novel ensemble approach for vortex dipoles and loops, deriving effective sine-Gordon theories and connecting the Abelian Higgs model to compact QED with screening.

Findings

Derived representations of partition functions for vortex ensembles.

Calculated bilocal correlator of vortex dipoles in the low-energy limit.

Established equivalence to compact QED with Debye screening in the London limit.

Abstract

In the London limit of the Ginzburg-Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation- and translation invariant measure of integration over their shapes leads to effective sine-Gordon theories of the dual fields. The representations of the partition functions of both grand canonical ensembles are derived in the form of the integrals over the vortex dipoles and the small vortex loops, respectively. By virtue of these representations, the bilocal correlator of the vortex dipoles (loops) is calculated in the low-energy limit. It is further demonstrated that once the vortex dipoles (loops) are considered as such an ensemble rather than individual ones, the London limit of the Ginzburg-Landau theory (Abelian Higgs model) with external monopoles is equivalent up to the leading order in the inverse UV cutoff to the compact QED in the corresponding dimension with the charge of Cooper pairs changed due to the Debye screening.