Soluções BPS de vórtices e Skyrmions em teorias de calibre estendidas imersas em meios magnéticos

Abstract

In this thesis, I present three original contributions to solutions of Skyrmions and planar vortices using the BPS formalism. First, in the context of Skyrme models, we propose two original configurations that generate BPS solitons: the first in the baby Skyrme-Maxwell model and the second in the baby Skyrme-Born-Infeld model. In both scenarios, we introduce a function G(φn), called generalized permeability, together with the Maxwell and Born-Infeld terms, respectively. In both scenarios, from the minimization of the energy functional, we obtain general expressions for the minimum energy of the field configurations, as well as for the respective BPS equations, which depend directly on the structure of the permeabilities. We analyze the solutions of the modified models and compare them with the usual solutions, with the aim of identifying and highlighting the modification generated by the introduction of the non-trivial G functions. Finally, in the context of Maxwell-Chern-Simons electrodynamics, following the same procedure as the Skyrme models, we propose the extension of the model by means of the coupling of a new permeability. Now, the G(χ) function depends on an additional scalar field χ, whose dynamics is introduced in order to extend the symmetry of the original Lagrangian density, in addition to serving as a source field for vortex solutions.