Hopf solitons in the Nicole model

TL;DR

This paper numerically constructs and analyzes Hopf solitons in the Nicole model, revealing instability of symmetric solutions at higher charges and discovering new knotted and linked configurations.

Contribution

It introduces a volume-preserving flow method to find all Hopf charge solitons up to eight, uncovering new lower energy knotted and linked solutions beyond symmetric forms.

Findings

Axially symmetric solutions are unstable for Hopf charges > 2.

New knotted and linked solitons with lower energy are found.

Comparison with the Skyrme-Faddeev model shows universal features and some differences.

Abstract

The Nicole model is a conformal field theory in three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to numerically construct soliton solutions for all Hopf charges from one to eight. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than two and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.