Topological self-dual configurations in a Lorentz-violating gauged O(3) sigma model

TL;DR

This paper investigates self-dual topological configurations in a Lorentz-violating gauged O(3) sigma model, revealing new magnetic solutions with electric fields and flux reversion due to Lorentz-violating terms.

Contribution

It introduces Lorentz-violating terms into the gauged O(3) sigma model and analyzes their effects on self-dual configurations, including novel solutions with electric fields.

Findings

Self-dual configurations exist with properties similar to standard models.

Lorentz violation induces magnetic flux reversion.

New solutions carry electric fields with zero total electric charge.

Abstract

We have studied the existence of topological Bogomol'nyi-Prasad-Sommerfield or self-dual configurations in a Lorentz-violating gauged $O(3)$ nonlinear sigma model, where $CPT$-even Lorentz-violating (LV) terms were introduced in both the gauge and $\sigma $% -field sectors. As happens in the usual gauged $\sigma $ model, purely magnetic self-dual configurations are allowed, maintaining some qualitative features of the standard ones. In a more involved configuration, Lorentz violation provides new self-dual magnetic solutions carrying an electric field but a null total electric charge. In both cases, the total energy of the self-dual configurations turns out to be proportional to the topological charge of the model and to the LV parameters introduced in the $% \sigma $ sector. It is shown that the LV terms yield magnetic flux reversion as well.