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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
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
Citation:
Josh Cork, Derek Harland, “Geometry of Gauged Skyrmions”, SIGMA, 19 (2023), 071, 30 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1966 https://www.mathnet.ru/eng/sigma/v19/p71
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Abstract page: | 47 | Full-text PDF : | 10 | References: | 12 |
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