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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 071, 30 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.071
(Mi sigma1966)
 

Geometry of Gauged Skyrmions

Josh Corka, Derek Harlandb

a School of Computing and Mathematical Sciences, University of Leicester, University Road, Leicester, UK
b School of Mathematics, University of Leeds, Woodhouse Lane, Leeds, UK
References:
Abstract: A work of Manton showed how skymions may be viewed as maps between riemannian manifolds minimising an energy functional, with topologically non-trivial global minimisers given precisely by isometries. We consider a generalisation of this energy functional to gauged skyrmions, valid for a broad class of space and target $3$-manifolds where the target is equipped with an isometric $G$-action. We show that the energy is bounded below by an equivariant version of the degree of a map, describe the associated BPS equations, and discuss and classify solutions in the cases where $G=\mathrm{U}(1)$ and $G=\mathrm{SU}(2)$.
Keywords: skyrmions, topological solitons, BPS equations.
Received: March 12, 2023; in final form September 14, 2023; Published online October 1, 2023
Document Type: Article
MSC: 53C07, 70S15, 53C43
Language: English
Citation: Josh Cork, Derek Harland, “Geometry of Gauged Skyrmions”, SIGMA, 19 (2023), 071, 30 pp.
Citation in format AMSBIB
\Bibitem{CorHar23}
\by Josh~Cork, Derek~Harland
\paper Geometry of Gauged Skyrmions
\jour SIGMA
\yr 2023
\vol 19
\papernumber 071
\totalpages 30
\mathnet{http://mi.mathnet.ru/sigma1966}
\crossref{https://doi.org/10.3842/SIGMA.2023.071}
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