To be or knot to be?

TL;DR

This paper explores the existence and stability of knotted soliton solutions in a three-dimensional classical field theory, revealing a variety of stable configurations like toroids, links, and knots through analytical and numerical methods.

Contribution

It extends previous work by demonstrating a wide range of stable knotted and linked solitons for charges 1 to 8 using advanced analytical and numerical techniques.

Findings

Stable toroidal solitons with twists identified

Linked loops and knots observed as stable solutions

Reconnection of string-like segments enables diverse phenomena

Abstract

It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended this work in some detail using a combination of analytic approximations and sophisticated numerical algorithms. For charges between one and eight, we find solutions which exhibit a rich and spectacular variety of phenomena, including stable toroidal solitons with twists, linked loops and also knots. The physical process which allows for this variety is the reconnection of string-like segments.