Geometry of Gauged Skyrmions

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 $G=\mathrm{SU}(2)$.

References in corpus (4)

• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• The Dielectric Skyrme model
• Solitons in the Gauged Skyrme-Maxwell Model
• Some aspects of Skyrme--Chern-Simons densities