Background fields and self-dual Skyrmions

Abstract

We show that a suitable background field can bring a non-BPS topological soliton into its Bogomol'nyi-Prasad-Sommerfield (BPS), self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g., solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background.