Strings and skyrmions on domain walls

TL;DR

This paper investigates domain walls with localized orientational moduli and skyrmions on them, providing analytic solutions and effective actions within a simple model, and analyzing their symmetries and configurations.

Contribution

It introduces a simple model with domain walls hosting orientational moduli and skyrmions, including analytic solutions and effective theories, expanding understanding of topological defects on domain walls.

Findings

Existence of domain walls with localized orientational moduli.

Construction of skyrmion solutions on domain walls.

Derivation of effective action in the low-energy limit.

Abstract

We address a simple model allowing the existence of domain walls with orientational moduli localized on them. Within this model, we discuss an analytic solution and explore it in the context of previously known results. We discuss the existence of one-dimensional domain walls localized on two-dimensional ones, and construct the corresponding effective action. In the low-energy limit, which is the $\mathbb{O}(3)$ sigma-model, we discuss the existence of skyrmions localized on domain walls, and provide a solution for a skyrmion configuration, based on an analogy with instantons. We perform symmetry analysis of the initial model and of the low-energy theory on the domain wall world volume.