Skyrmions from Instantons inside Domain Walls

TL;DR

This paper demonstrates how Skyrmions can be realized as instantons confined within domain walls in a five-dimensional gauge theory, with the wall's worldvolume dynamics described by the Skyrme model.

Contribution

It provides a dynamical realization of the Atiyah-Manton construction, connecting instantons inside domain walls to Skyrmions in a novel five-dimensional gauge theory framework.

Findings

Instantons are localized inside domain walls.

The worldvolume theory of the wall is described by the Skyrme model.

Instantons appear as Skyrmions within the domain wall.

Abstract

Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the worldvolume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as Skyrmions.