Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 071, 30 pages      arXiv:2303.02623      https://doi.org/10.3842/SIGMA.2023.071
Contribution to the Special Issue on Topological Solitons as Particles

Geometry of Gauged Skyrmions

Josh Cork a and Derek Harland b
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

Received March 12, 2023, in final form September 14, 2023; Published online October 01, 2023

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 $G={\rm U}(1)$ and $G={\rm SU}(2)$.

Key words: skyrmions; topological solitons; BPS equations.

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