On the topological charge of $SO(2)$ gauged Skyrmions in $2+1$ and $3+1$ dimensions

Abstract

The question of the dependence of the topological charge $q$ of a gauged Skyrmion, on the gauge field, is studied quantitatively. Two examples, both gauged with $SO(2)$ are studied and contrasted: i) The $O(3)$ model in $2+1$ dimensions, and ii) The $O(4)$ model in $3+1$ dimensions. In case i), where the (usual) Chern-Simons (CS) term is present, the value of $q$ changes sign, going through zero. This evolution is tracked by a parameter characterising the solutions in the given theory. In case ii), in which dimensions no CS density is available, the evolution of $q$ is not observed.

12 pages, 7 figures; new references added

References in corpus (5)

• Stationary ring solitons in field theory - knots and vortons
• Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence
• Gauged Baby Skyrme Model with Chern-Simons term
• The effect of Chern-Simons dynamics on the energy of electrically charged and spinning vortices
• Vortices of $SO(2)$ gauged Skyrmions in $2+1$ dimensions

Cited by in corpus (6)

• Vortices of $SO(2)$ gauged Skyrmions in $2+1$ dimensions
• Solitons in the Gauged Skyrme-Maxwell Model
• Some aspects of Skyrme--Chern-Simons densities
• On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in $d=4+1$ dimensions
• $SO(2)$ gauged Skyrmions in $4+1$ dimensions
• Geometry of Gauged Skyrmions