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

Francisco Navarro-Lerida; Eugen Radu; D. H. Tchrakian

doi:10.1016/j.physletb.2019.02.011

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arXiv · 1811.09535

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

Francisco Navarro-Lerida·Eugen Radu·D. H. Tchrakian

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Abstract

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 $3+1$ dimensions. 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.

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Francisco Navarro-Lerida, Eugen Radu, D. H. Tchrakian. 2018-11-23. On the topological charge of $SO(2)$ gauged Skyrmions in $2+1$ and $3+1$ dimensions. https://doi.org/10.1016/j.physletb.2019.02.011

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