Solitons, Links and Knots

TL;DR

This paper uses numerical simulations to explore complex topological solitons in a modified O(3) sigma model, revealing structures like strings, links, and knots stabilized by Hopf charge, with string reconnection as a key mechanism.

Contribution

It demonstrates the formation of diverse topological solitons, including knots and links, in a three-dimensional model, highlighting the role of string reconnection in their structure.

Findings

Solitons up to charge five are closed strings with increasing twist.

Higher charge solitons form linked loops and knots.

String reconnection is crucial for the formation of complex solitons.

Abstract

Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for solitons up to charge five the solutions have the structure of closed strings, which become increasingly twisted as the charge increases. However, for higher charge the solutions are more exotic and comprise linked loops and knots. We discuss the structure and formation of these solitons and demonstrate that the key property responsible for producing such a rich variety of solitons is that of string reconnection.