Electrically Charged Two-Dimensional Skyrmions

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The (2 + 1)-dimensional Skyrme gauge model with a Chern–Simons term is considered. The presence of the Chern–Simons term leads to the result that the Abelian gauge field of the model becomes massive. This, in turn, leads to the existence in the given model of two-dimensional skyrmions carrying magnetic flux and possessing an electric charge and, consequently, nonzero angular momentum. It is shown that the model also admits the existence of two-dimensional skyrmions, whose electrically charged fields rotate with a constant phase frequency. Due to the nontrivial topology of the configurations of the (2 + 1)-dimensional Skyrme gauge model with a Chern–Simons term, the magnetic flux, the electric charge, and the angular momentum of a rotating two-dimensional skyrmion turn out to be interrelated.