Soliton stability in some knot soliton models

TL;DR

This paper investigates the stability of knotted soliton solutions in non-linear field theories, revealing that in some models different topological sectors are not separated by energy barriers, affecting their stability and existence.

Contribution

It provides a detailed analysis of soliton stability in the AFZ and Nicole models, highlighting differences in topological sector separation and the implications for soliton existence.

Findings

In the AFZ model, different topological sectors are not separated by infinite energy barriers.

Static solutions in the AFZ model are not critical points if topological charge varies.

In the Nicole model, different topological sectors are separated by infinite energy barriers.

Abstract

We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.