Abstract
We show that a suitable background field can bring a non-BPS topological soliton into its 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.
Highlights
We show that a suitable background field can bring a non-BPS topological soliton into its Bogomol'nyiPrasad-Sommerfield (BPS), self-dual, counterpart
A detailed understanding of interactions of topological solitons, that is, localized particle-like solutions of nonlinear field equations, which carry a nontrivial value of a topological charge [1,2], is a great challenge of contemporary physics
Any background field deformation of the minimal Skyrme model which leads to Bogomol’nyi equations such that the resulting eigenvalues are uniquely defined by the background field implies a triviality of the moduli space
Summary
A detailed understanding of interactions of topological solitons, that is, localized particle-like solutions of nonlinear field equations, which carry a nontrivial value of a topological charge [1,2], is a great challenge of contemporary physics. For such a self-dual deformed model, the lowest order annihilation (scattering) process occurs as a geodesic flow on a certain moduli space This allowed for a systematical understanding of the role of internal modes [8] (which in the deformed model nontrivially depend on the position on the moduli space) in SAS dynamics leading to the discovery of spectral walls [9,10]. The importance of this self-dual background field framework is related to the fact that it can be applied to any multisolitonic scattering provided the initial as well as the final states are self-dual solitons. As a particular example we consider the minimal Skyrme model in (3 þ 1) dimensions
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