Skyrmions from Instantons inside Domain Walls

TL;DR

It is shown that the world volume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as domain wall Skyrmions.

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.

Figures (1)

• Figure 1: The three layer structure of the domain wall when $e^2v^2\ll m^2$.