Abstract
Vortices the $SO(2)$ gauged planar Skyrme model, with a) only Maxwell, b) only Chern-Simons, and c) both Maxwell and Chern-Simons dynamics are studied systematically. In cases a) and b), where both models feature a single parameter $\lambda$ (the coupling of the potential term), the dependence of the energy on $\lambda$ is analysed. It is shown that the plots of the energy $vs.$ $\lambda$ feature discontinuities and branches. In case c), the emphasis is on the evolution of the topological charge, taking non-integer values. Throughout, the properties studied are contrasted with those of the corresponding Abelian Higgs models.
Highlights
Solitons of the gauged Skyrme model, Skyrmions, present much more complex properties than their Higgs counterparts, e.g., the Abelian Higgs vortices in 2 þ 1 dimensions [1], monopoles in 3 þ 1 dimensions [2,3] and monopoles in D þ 1 dimensions [4]
While in the previous two sections our attention was focused on the energy profiles vs λ, the dimensionless constant parametrizing the coupling of the potential, here instead we focus on the evolution of the topological charge in a given Maxwell–Chern-Simons–Skyrme theory
The studies in (a) and (b) are aimed at exposing discontinuities and branchings in the energy profiles of such solutions, which were encountered in the solutions to the SOð3Þ gauged Oð4Þ Skyrme model on R3
Summary
Solitons of the gauged Skyrme model, Skyrmions, present much more complex properties than their Higgs counterparts, e.g., the Abelian Higgs vortices in 2 þ 1 dimensions [1], monopoles in 3 þ 1 dimensions [2,3] and monopoles in D þ 1 dimensions [4]. The first objective is to reveal the peculiar dependence of the energy on a parameter in the model, that is typical of gauged Skyrmions This has been studied in the case of the SOð3Þ gauged Skyrmion on R3, namely the Oð4Þ sigma model, where the energy was plotted against the coupling of the (quartic kinetic) Skyrme term. It was found in [19,20] and in [21] that the energy profile exhibited discontinuities and branches. To achieve our second objective, we employ the model (c) incorporating both Maxwell and Chern-Simons terms, i:e., with nonvanishing couplings β and κ in (1) This is the simplest system which enables the tracking of the topological charge leading to its annihilation. For the definition of the familiar global charges, we refer to Ref. [9]
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