Skyrmions and domain walls in (2+1) dimensions

TL;DR

This paper investigates classical solutions in a (2+1)-dimensional O(3) sigma model, revealing Skyrmions and domain walls, their interactions, and wave propagation, including topologically charged waves and Skyrmion emission from walls.

Contribution

It demonstrates the existence of stable domain walls and Skyrmion solutions in a (2+1)D sigma model, and explores their dynamic interactions and wave phenomena.

Findings

Stable domain walls connect different vacua.

Waves carrying topological charge can propagate on walls.

Walls can absorb and emit Skyrmions under certain conditions.

Abstract

We study classical solutions of the vector O(3) sigma model in (2+1) dimensions, spontaneously broken to O(2)xZ2. The model possesses Skyrmion-type solutions as well as stable domain walls which connect different vacua. We show that different types of waves can propagate on the wall, including waves carrying a topological charge. The domain wall can also absorb Skyrmions and, under appropriate initial conditions, it is possible to emit a Skyrmion from the wall.