Skyrmions and Faddeev-Hopf Solitons

TL;DR

This paper explores a family of generalized Skyrme models, revealing how Skyrmions transition from polyhedral shapes to loop-like structures as parameters vary, connecting different topological solitons.

Contribution

It introduces a one-parameter family of models unifying Skyrmions and Hopf solitons, analyzing their minimal-energy solutions and shape transformations.

Findings

Skyrmions resemble polyhedral shells

Hopf solutions look like linked loops

Shape deformation depends on model parameters

Abstract

This paper describes a natural one-parameter family of generalized Skyrme systems, which includes the usual SU(2) Skyrme model and the Skyrme-Faddeev system. Ordinary Skyrmions resemble polyhedral shells, whereas the Hopf-type solutions of the Skyrme-Faddeev model look like closed loops, possibly linked or knotted. By looking at the minimal-energy solutions in various topological classes, and for various values of the parameter, we see how the polyhedral Skyrmions deform into loop-like Hopf Skyrmions.