Topological symmetry breaking and the confinement of anyons

TL;DR

This paper investigates how topological symmetry breaking in a 2+1D Abelian-Higgs model with Chern-Simons term leads to confinement of anyons through long-range interactions caused by instanton linking.

Contribution

It introduces a novel analysis of topological symmetry breaking effects on anyon confinement using Wilson and 't Hooft loops in a Chern-Simons-modified Abelian-Higgs model.

Findings

Long-range confining potential between electric charges and flux tubes.

Confinement of anyons due to topological linking of instantons.

Perturbative forces remain short-range despite confinement.

Abstract

We study topological symmetry breaking via the behaviour of Wilson and 't Hooft loop operators for the 2+1 dimenesional Abelian-Higgs model with Chern-Simons term. The topological linking of instantons, which are closed vortex loop configurations, give rise to a long-range, logarithmic, confining potential between electric charges and magnetic flux tubes even though all perturbative forces are short range. Gauss' law forces the concomitance of charge and magnetic flux, hence the confinement is actually of anyons.