Classically Isospinning Hopf Solitons

TL;DR

This study numerically investigates how isospinning Hopf solitons in the Skyrme-Faddeev model deform and change their spectrum when isospin is introduced, revealing new solution types and shape transformations.

Contribution

It provides the first detailed numerical analysis of deformations and spectrum rearrangements of isospinning Hopf solitons with charges up to 8.

Findings

Isospinning solitons can break symmetries of static solutions.

The shape of the lowest energy soliton can change with isospin.

New solution types and spectrum transmutations occur when isospin is added.

Abstract

We perform full three-dimensional numerical relaxations of isospinning Hopf solitons with Hopf charge up to 8 in the Skyrme-Faddeev model with mass terms included. We explicitly allow the soliton solution to deform and to break the symmetries of the static configuration. It turns out that the model with its rich spectrum of soliton solutions, often of similar energy, allows for transmutations, formation of new solution types and the rearrangement of the spectrum of minimal-energy solitons in a given topological sector when isospin is added. We observe that the shape of isospinning Hopf solitons can differ qualitatively from that of the static solution. In particular the solution type of the lowest energy soliton can change. Our numerical results are of relevance for the quantization of the classical soliton solutions.