SELF-DUAL NON-ABELIAN VORTICES IN A $\PHI^2$ CHERN-SIMONS THEORY

TL;DR

This paper investigates non-Abelian Chern-Simons vortices in 2+1 dimensions with anomalous magnetic interactions, deriving self-dual equations and analyzing their properties, including flux quantization and non-topological nature.

Contribution

It introduces a specific relation between CS mass and magnetic coupling that simplifies the equations to first order and derives self-dual vortex solutions with unique flux and charge properties.

Findings

Vortex solutions carry non-quantized magnetic flux.

Electric charge and angular momentum are quantized due to CS term.

Equations reduce to pure CS type under certain conditions.

Abstract

We study a non-Abelian Chern-Simons gauge theory in $ 2+ 1$ dimensions with the inclusion of an anomalous magnetic interaction. For a particular relation between the Chern-Simons (CS) mass and the anomalous magnetic coupling the equations for the gauge fields reduce from second- to first order differential equations of the pure CS type. We derive the Bogomol'nyi-type or self-dual equations for a $\bphi^2$ scalar potential, when the scalar and topological masses are equal. The corresponding vortex solutions carry magnetic flux that is not quantized due to the non-toplogical nature of the solitons. However, as a consequence of the quantization of the CS term, both the electric charge and angular momentum are quantized.