Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory

TL;DR

This paper develops a framework for understanding symmetry breaking and confinement in 2+1-dimensional gauge theories with quantum group symmetries, revealing how electric and magnetic condensates lead to confinement phenomena.

Contribution

It introduces a general theory of symmetry breaking applicable to models with quantum group symmetries, unifying electric and magnetic condensate effects in 2+1D gauge theories.

Findings

Electric condensates lead to magnetic confinement.

Magnetic condensates cause electric confinement.

The formalism is illustrated with electric, magnetic, and dyonic condensate examples.

Abstract

Gauge theories in 2+1 dimensions whose gauge symmetry is spontaneously broken to a finite group enjoy a quantum group symmetry which includes the residual gauge symmetry. This symmetry provides a framework in which fundamental excitations (electric charges) and topological excitations (magnetic fluxes) can be treated on equal footing. In order to study symmetry breaking by both electric and magnetic condensates we develop a theory of symmetry breaking which is applicable to models whose symmetry is described by a quantum group (quasitriangular Hopf algebra). Using this general framework we investigate the symmetry breaking and confinement phenomena which occur in (2+1)-dimensional gauge theories. Confinement of particles is linked to the formation of string-like defects. Symmetry breaking by an electric condensate leads to magnetic confinement and vice-versa. We illustrate the general formalism with examples where the symmetry is broken by electric, magnetic and dyonic condensates.