Exact Self-dual Soliton Solutions in a Gauged O(3) Sigma Model with Anomalous Magnetic Moment Interaction

TL;DR

This paper demonstrates that a gauged nonlinear O(3) sigma model with anomalous magnetic moment interaction in 2+1 dimensions admits exact self-dual soliton solutions, which can be mapped to Abelian magnetic vortices, revealing integrability and novel solution structures.

Contribution

It introduces an exactly integrable gauged nonlinear O(3) sigma model with anomalous magnetic moment interaction and establishes a mapping to Abelian magnetic vortex solutions.

Findings

Exact self-dual soliton solutions are obtained.

Static matter fields are equivalent to ungauged models.

Solutions can be mapped to Abelian magnetic vortices.

Abstract

It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous magnetic moment interaction in $2+1$ dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the usual ungauged nonlinear $O(3)$ sigma model. These static soliton solutions can be mapped into an Abelian purely magnetic vortex solutions through a suitable reduction of the non-Abelian gauge group. A relativistic Abelian model in $2+1$ dimensions is also presented where these purely magnetic vortices can be realized.