Topological and self-dual vortices in a double sigma model with Maxwell coupling

TL;DR

This paper constructs a double O(3)-sigma model coupled to Maxwell fields in (2+1) dimensions, revealing self-dual vortex solutions with quantized flux and analyzing their topological and energetic properties.

Contribution

It introduces a novel double sigma model with Maxwell coupling, demonstrating the existence and properties of self-dual magnetic vortices in this framework.

Findings

Existence of self-dual vortex solutions with quantized magnetic flux.

Both sigma fields belong to the same topological sector in the BPS regime.

Numerical solutions show smooth, localized field profiles with regular energy density.

Abstract

In this work, we construct a double O(3)-sigma model minimally coupled to a Maxwell field in (2+1)-dimensional spacetime and investigate the existence of self-dual magnetic vortex solutions. An analysis of the Bogomol'nyi-Prasad-Sommerfield (BPS) property reveals that both sigma fields belong to the same topological sector and that the potential assumes a periodic cosine-like form. Furthermore, the theory supports the emergence of magnetic vortices with quantized flux, described by two nonlinear O(3)-sigma sectors that effectively combine into a single topological sector in the BPS regime. In addition, we analytically verify the consistency of the BPS structure and its asymptotic behavior. Within this framework, numerical vortex solutions confirm that the field profiles are smooth and spatially localized, with both the magnetic field and the energy density remaining regular and localized.