Confined Vortices in Topologically Massive U(1)$\times$U(1) Theory

TL;DR

This paper introduces a new topological vortex solution in U(1)×U(1) Maxwell-Chern-Simons theory, revealing unique properties like classical confinement and non-integer charges, with implications for understanding vortex behavior in gauge theories.

Contribution

The paper presents the first vortex solution with non-integer charges in a topologically massive U(1)×U(1) theory, expanding the landscape of known vortex configurations.

Findings

Vortices exhibit long-range forces due to unbroken U(1) in the infrared.

Ensemble of vortices must have zero total winding number to avoid divergent energy.

Higher winding solutions carry non-integer charges, a novel feature.

Abstract

We report on a new topological vortex solution in U(1)$\times$U(1) Maxwell-Chern-Simons theory. The existence of the vortex is envisaged by analytical means, and a numerical solution is obtained by integrating the equations of motion. These vortices have a long-range force because one of the U(1)s remains unbroken in the infrared, which is guarded by the Coleman-Hill theorem. The sum of the winding numbers of an ensemble of vortices has to vanish; otherwise the system would have a logarithmically divergent energy. In turn, these vortices exhibit classical confinement. We investigate the rich parameter space of the solutions, and show that one recovers the Abrikosov-Nielsen-Olesen, U(1) Maxwell-Chern-Simons, U(1) pure Chern-Simons and global vortices as various limiting cases. Unlike these limiting cases, the higher winding solutions of our vortices carry non-integer charges under the broken U(1). This is the first vortex solution exhibiting such behavior.