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 (12)

• A Skyrme-type proposal for baryonic matter
• Topological energy bounds for the Skyrme and Faddeev models with massive pions
• Static solutions in the U(1) gauged Skyrme model
• Spinning U(1) gauged Skyrmions
• SO(3) Gauged Soliton of an O(4) Sigma Model on $R_3$
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• The Dielectric Skyrme model
• Monopoles and dyons in SO(3) gauged Skyrme models
• On the topological charge of $SO(2)$ gauged Skyrmions in $2+1$ and $3+1$ dimensions
• Solitons in the Gauged Skyrme-Maxwell Model
• On the geometry of magnetic Skyrmions on thin films
• Some aspects of Skyrme--Chern-Simons densities