We study the simplest S O ( 2 ) gauged O ( 5 ) Skyrme model in 4 + 1 (flat) dimensions. In the gauge decoupled limit, the model supports topologically stable solitons (Skyrmions) and after gauging, the static energy of the solutions is bounded from below by a “baryon number.” The studied model features both Maxwell and Maxwell–Chern-Simons dynamics. The considered configurations are subject to biazimuthal symmetry in the R 4 subspace resulting in a two dimensional subsystem, as well as subject to an enhanced symmetry relating the two planes in the R 4 subspace, which results in a one dimensional subsystem. Numerical solutions are constructed in both cases. In the purely magnetic case, fully biazimuthal solutions were given, while electrically charged and spinning solutions were constructed only in the radial (enhanced symmetric) case, both in the presence of a Chern-Simons term, and in its absence. We find that, in contrast with the analogous models in 2 + 1 dimensions, the presence of the Chern-Simons term in the model under study here results only in quantitative effects.
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