Self-dual solitons in a Maxwell-Chern-Simons baby Skyrme model

TL;DR

This paper investigates self-dual solitons in a gauged baby Skyrme model with Maxwell-Chern-Simons dynamics, revealing two types of decay profiles, quantized topological charge, and unique magnetic flux inversion phenomena.

Contribution

It develops a detailed Bogomol'nyi-Prasad-Sommerfield formalism for the Maxwell-Chern-Simons gauged baby Skyrme model, identifying new soliton solutions with distinctive properties.

Findings

Two types of self-dual Skyrme field profiles: exponential and power-law decay.

Topological charge is quantized, but magnetic flux and electric charge are not.

Discovery of localized magnetic flux inversion not seen in previous models.

Abstract

We have studied the existence de self-dual solitons in a gauged version of the baby Skyrme model in which the gauge field dynamics is governed by the Maxwell-Chern-Simons action. For such a purpose, we have developed a detailed implementation of the Bogomol'nyi-Prasad-Sommerfield formalism providing the self-dual equations whose solutions saturate the energy lower bound. Such a bound related to the topological charge of the Skyrme field becomes quantized whereas both the total magnetic flux and the total electrical charge are not. We have found two types of self-dual Skyrme field profiles: the first is described by a solution which decays following an exponential-law ($e^{-\alpha r^2}$, $\alpha>0$); the second is portrayed by a solution having a power-law decay ($r^{-\beta}$, $\beta>0$). On other hand, in both cases the asymptotic behavior of the gauge field is similar to the one presented in the context of the Abelian Higgs models describing Abrikosov-Nielsen-Olesen charged vortices. Other interesting feature we highlight is the localized magnetic flux inversion, a property does not observed in others gauged baby Skyrme models already studied in literature. Numerical results are presented for rotationally symmetrical field configurations by remarking some of its essential features.