On the topological charge of S O (2) gauged Skyrmions in 2+1 and 3+1 dimensions

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The question of the dependence of the topological charge q of a gauged Skyrmion, on the gauge field, is studied quantitatively. Two examples, both gauged with SO (2) are studied and contrasted: i) The O (3) model in 2 + 1 dimensions, and ii) The O(4) model in 3 + 1dimensions. In case i), where the (usual) Chern-Simons (CS) term is present, the value of q changes sign, going through zero. This evolution is tracked by a parameter characterising the solutions in the given theory. In case ii), in which dimensions no CS density is available, the evolution of q is not observed. (C) 2019 The Author(s). Published by Elsevier B.V.
© 2019 The Author(s). Published by Elsevier B.V. We are very grateful to V. A. Rubakov for valuable and penetrating comments. E. R. gratefully acknowledges the support of DIAS. The work of E. R. was also partially supported by the Portuguese national funding agency for science, research and technology (FCT), within the Center for Research and Development in Mathematics and Applications (CIDMA), project UID/MAT/04106/2019, and also by the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904, 11This phenomenon is observed also in (gauged) Higgs theories, where the Chern-Simons (CS) dynamics is supplied by Higgs-CS[14](HCS) terms, reported in Refs.[27,28]. the H2020-MSCA-RISE-2017 Grant No. FunFiCO-777740, and by the CIDMA project UID/MAT/04106/2013. The numerical computations in Section3were performed at the BLAFIS cluster in Aveiro University.
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