A Note on Gauged Baby Skyrmions

Abstract

AbstractIn this paper we study a gauged version of the two dimensional Skyrme model of nuclear physics; the field configurations are couples (u, A), where $$u:{\mathbb {R}}^2\rightarrow S^2$$ u : R 2 → S 2 is a map constant at infinity, which can be classified by its topological degree, and $$A:{\mathbb {R}}^2\rightarrow {\mathbb {R}}^2$$ A : R 2 → R 2 is the gauge field. We prove the existence of rotationally symmetric field configurations which minimize the gauged Skyrme energy on every topological sector (gauged baby skyrmions). Moreover we study the behavior of these skyrmions in the case of weak or strong coupling with the gauge field. In particular, we show that, as observed by many authors by means of numerical simulations, in the strong coupling regime the magnetic flux associated with the gauge field becomes quantized.