Restricted baby Skyrme-Maxwell theory in a magnetic medium: BPS configurations and some properties

TL;DR

This paper investigates BPS configurations in a restricted baby Skyrme-Maxwell model with magnetic permeability, deriving conditions for solutions, analyzing their properties, and presenting exact solutions with rotational symmetry.

Contribution

It introduces a method to find BPS solutions in a modified baby Skyrme-Maxwell model including magnetic permeability, with analytical and numerical analysis of their properties.

Findings

Derived BPS equations and energy bounds for the model.

Found conditions for existence of BPS solutions.

Presented a family of exact BPS solutions.

Abstract

We study the existence of BPS configurations in a restricted baby Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic permeability. In order to attain such a goal, we use the Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the lower bound for the energy and the BPS equations whose [electrically neutral] solutions saturate that bound. During the energy minimization procedure, we find a differential constraint which involves the self-dual potential, the superpotential itself and also the magnetic permeability. In order to solve the BPS system, we focus our attention on those solutions with rotational symmetry. For that, we fix the magnetic permeability and select two BPS potentials which exhibit a similar behavior near to the vacuum. We depict the resulting profiles and proceed to an analytical description of the properties of the BPS magnetic field. Furthermore, we consider some essential aspects of our model, such as the conditions for the overall existence of the BPS solutions, and how the permeability affects the magnetic flux. Finally, we present a family of exact BPS solutions.