New class of solutions in the non-minimal O(3)-sigma model

TL;DR

This paper introduces a non-canonical O(3)-sigma model with non-minimal coupling, revealing new vortex solutions, kink configurations, and solitary waves, and analyzing their physical relevance and localization properties.

Contribution

It develops a novel non-canonical O(3)-sigma model with a dielectric-modified Maxwell term and explores its vortex and kink solutions using the BPS formalism.

Findings

Existence of vortex solutions with step-function profiles.

Emergence of solitary wave solutions similar to KdV structures.

Localization effects making some vortex solutions non-physical.

Abstract

For the study of topological vortices with non-minimal coupling, we built a kind of non-canonical O(3)-sigma model, with a Maxwell term modified by a dielectric function. Through the BPS formalism, an investigation is made on possible configurations of vortices in topological sectors of the sigma model and the real scalar field. For a particular ansatz, the solutions of the topological sector of the real scalar field are described by the known kink solutions. On the other hand, when studying the vortices in the non-minimal sector of the pure O(3)-sigma model, it is detected the emergence of solutions that generate solitary waves similar to structures derived from a KdV-like theory. We observed that in the study of mixed models, namely, the topological sector of the O(3)-sigma model coupled to the topological sector of the real scalar field, the vortex solutions assume a profile of a step function. Then, when kinks of the topological sector of the scalar field are interacting with the field of the sigma model, it makes the field solutions of the O(3)-sigma model become extremely localized, making the vortice structures non-physical.