Relations among topological solitons

TL;DR

This paper explores the interrelations among various topological solitons across different dimensions, constructing complex composite configurations and revealing how simpler solitons can form intricate nested structures.

Contribution

It introduces a unified framework for understanding relations among diverse topological solitons and constructs a comprehensive composite soliton configuration.

Findings

Constructed a composite wall-vortex-monopole-instanton configuration

Derived all possible nested soliton configurations from the composite

Established relations among topological solitons across dimensions

Abstract

We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby Skyrmion (lump) and Skyrmion. We construct a composite configuration consisting of a domain wall, vortex, magnetic monopole and Yang-Mills instanton (wall-vortex-monopole-instanton) using the effective theory technique or moduli approximation. Removing some solitons from such a composite, we obtain all possible composite solitons in the form of solitons within a soliton, including all the previously known configurations, yielding relations among topological solitons.