Topological Chern-Simons vortices in the $O(3) \sigma$-model

TL;DR

This paper investigates topologically stable, anyonic vortices in a (2+1)-dimensional gauged $O(3) \sigma$-model with a Chern--Simons term, analyzing their properties through analytic and numerical methods.

Contribution

It introduces a new model with Chern--Simons term, providing analytic approximations and numerical solutions for vortex properties and interactions.

Findings

Vortices exhibit topological stability and anyonic statistics.

Vortex mass and charge depend on gauge coupling.

Bound states of vortices are identified with varying masses.

Abstract

We present a (2+1)-dimensional gauged $O(3) \sigma$-model with an Abelian Chern--Simons term. It shows topologically stable, anyonic vortices as classical solutions. The fields are studied in the case of rotational symmetry and analytic approximations are found for their asymptotic behaviour. The static Euler--Lagrange equations are solved numerically, where particular attention is paid to the dependence of the vortex' properties on the coupling to the gauge field. We compute the vortex mass and charge as a function of this coupling and obtain bound states for two--vortices as well as two--vortices with masses above the stability threshold.