Correspondence between Skyrmions in 2+1 and 3+1 Dimensions

TL;DR

This paper explores the relationships between Skyrmions in 2+1 and 3+1 dimensions, constructing various types of Skyrmions within domain walls in different sigma models, revealing their interconnected structures.

Contribution

It introduces explicit constructions of 3D Skyrmions as lumps and baby Skyrmions inside non-Abelian domain walls, establishing a correspondence between lower and higher-dimensional Skyrmions.

Findings

Constructed a BPS 3D Skyrmion as a lump inside a non-Abelian domain wall.

Realized a conventional 3D Skyrmion as a baby Skyrmion in a modified Skyrme model.

Demonstrated a spinning 3D Skyrmion as a Q-lump within a domain wall.

Abstract

A lump (2D Skyrmion) can be constructed as a sine-Gordon kink (1D Skyrmion) inside a domain wall in the massive O(3) sigma model. In this paper, we discuss relations between Skyrmions in 2+1 and 3+1 dimensions. We first construct a Bogomol'nyi-Prasad-Sommerfield 3D Skyrmion as a lump inside a non-Abelian domain wall in an O(4) sigma model with a potential term admitting two discrete vacua. Next, we construct a conventional 3D Skyrmion as a baby Skyrmion in a non-Abelian domain wall in the Skyrme model with a modified mass term admitting two discrete vacua. We also construct a spinning 3D Skyrmion as a Q-lump in the non-Abelian domain wall.