Incarnations of Skyrmions

TL;DR

This paper explores various transformations of Skyrmions within different solitonic environments, revealing new confined states and their theoretical and numerical descriptions, expanding understanding of Skyrmion behavior in field theories.

Contribution

It introduces the concept of transforming Skyrmions into sine-Gordon kinks confined by vortices and constructs a Skyrmion as a twisted vortex ring, broadening the scope of Skyrmion configurations.

Findings

Skyrmions can be confined as sine-Gordon kinks by vortices.

Confined Skyrmions do not require higher-derivative terms in flat host solitons.

A Skyrmion can be realized as a twisted vortex ring with sixth-order derivatives.

Abstract

Skyrmions can be transformed into lumps or baby-Skyrmions by being trapped inside a domain wall. Here we find that they can also be transformed into sine-Gordon kinks when confined by vortices, resulting in confined Skyrmions. We show this both by an effective field theory approach and by direct numerical calculations. The existence of these trapped and confined Skyrmions does not rely on higher-derivative terms when the host solitons are flat or straight. We also construct a Skyrmion as a twisted vortex ring in a model with a sixth-order derivative term.