Gauged Sigma Models and Magnetic Skyrmions

Abstract

We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities

20 pages, version published in SciPost Physics on 10 September 2019; this version contains additional details regarding the application to magnetic skyrmions and impurities relative to the first arXiv version

References in corpus (1)

• BPS soliton-impurity models and supersymmetry

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