Estrutura BPS em teorias de calibre abelianas com derivadas de ordem superior

Abstract

The dissertation discusses the existence of BPS-like vortices (of the Abrikosov-Nielsen-Olesen type) in Abelian gauge models having high derivatives, where the gauge sector is the one that gains higher derivative terms. First, the study of vortex-like solutions in Podolsky-Higgs (PH) electrodynamics, the extension of Maxwell’s electrodynamics to high derivatives proposed by Boris Podolsky with the addition of the term of spontaneous symmetry breaking, was addressed. In the absence of the Podolsky term, the model reduces to that of Maxwell-Higgs (MH). The PH electrodynamics only presents BPS vortices if the Podolsky mass (m) is greater than or equal to twice the mass of the BPS vortices originated in the MH model. The second model describes a high-derived version of the Chern-Simons (CS) model which we will call Deser-Jackiw-Chern-Simons-Higgs (DJCSH) electrodynamics, the high-derivative term, called the Deser-Jackiw (DJ) action. The model includes BPS vortices loaded from a minimum value of the DJ mass (∆), this minimum value being a function of the other parameters of the model. An important consequence arising from the higher derivative terms, in both models, is that the respective BPS potentials become non local.