Knotted domain strings

TL;DR

This paper constructs stable knotted domain strings on torus-shaped solitons in 3+1 dimensions, demonstrating that all (p,q)-torus knots can be realized as linked domain and anti-domain strings in a Z2 Wess-Zumino model.

Contribution

It introduces a method to realize all (p,q)-torus knots as linked domain and anti-domain strings on solitons, expanding the understanding of topological structures in field theories.

Findings

All (p,q)-torus knots can be realized as linked domain strings.

Construction of meta-stable knotted domain strings on torus-shaped solitons.

Application to Z2 Wess-Zumino-type domain walls.

Abstract

We construct meta-stable knotted domain strings on the surface of a soliton of the shape of a torus in 3+1 dimensions. We consider the simplest case of Z2 Wess-Zumino-type domain walls for which we can cover the torus with a domain string accompanied with an anti-domain string. In this theory, all (p,q)-torus knots can be realized as a linked pair of a(n) (un)knotted domain string and an anti-domain string.