Non-Abelian Moduli on Domain Walls

TL;DR

This paper investigates a model with domain walls that have non-Abelian orientational moduli, explores the low-energy effective theory on the wall, and examines the effects of adding a spin-orbit interaction in the bulk.

Contribution

It introduces a simple model with non-Abelian moduli on domain walls, analyzes the low-energy $O(3)$ sigma model, and studies the impact of bulk spin-orbit interaction.

Findings

Numerical solutions for the wall profile functions.

Derivation of the $O(3)$ sigma model coupling in terms of bulk parameters.

Identification of entanglement between rotational and translational moduli due to spin-orbit interaction.

Abstract

We study a simple model supporting domain walls which possess two orientational moduli in addition to the conventional translational modulus. This model is conceptually close to Witten's cosmic strings. We observe an $O(3)$ sigma model on the wall world volume in the low-energy limit. We solve (numerically) classical static equations of motion and find the wall profile functions and the value of the coupling of the $O(3)$ model in terms of the bulk parameters. In the second part a term describing a spin-orbit interaction in the bulk is added, which gives rise to an entanglement between rotational and translational moduli. The corresponding extra term in the low-energy Lagrangian is calculated.