BPS solitons with internal structure in the gauged $O(3)$ sigma model

TL;DR

This paper explores self-dual solitons with internal structure in a gauged O(3) sigma model influenced by a dielectric medium, revealing how the medium alters soliton profiles through solutions of first-order equations.

Contribution

It introduces a novel analysis of solitons in a dielectric medium within the gauged O(3) sigma model using the BPS formalism, highlighting the impact of the medium on soliton structure.

Findings

Dielectric medium significantly modifies soliton profiles.

Internal structure affects energy bounds and solutions.

Solutions vary across different dielectric media.

Abstract

We investigate the existence of self-dual solitons with internal structure in a gauged $O(3)$ nonlinear sigma model immersed in a dielectric medium generated by a real scalar field (dubbed the source field). We consider rotationally symmetric configurations and applying the {Bogomol'nyi-Prasad-Sommerfield} formalism to obtain the energy lower bound and the respective {first-order differential equations (or self-dual equations).} By solving such a system of equations for three different dielectric media, we find the internal structure generates relevant changes in the soliton profiles when compared with the ones obtained without the presence of the dielectric medium.