Soluções auto-duais no modelo padrão estendido e em modelos generalizados

Abstract

We study self-dual con gurations solutions for gauge models in the context of the Standard Model Extension and in abelian Higgs generalized models. First we approach the Maxwell- Higgs model provided with Lorentz symmetry violation (VL) terms in two situations: In the rst case, we add the Carroll-Field-Jackiw (CPT-odd) term into the gauge sector and another CPT-even term in the Higgs sector. In the second case, we add CPT-even terms in both sectors. For both cases the Lorentz symmetry breaking terms modi ed the kinetic part of the eld. The con gurations in the presence of the Carroll-Field-Jackiw (CFJ) term have non-zero total electric charge as well as proportional to the magnetic ux, while the con gurations containing only CPT-even terms have null electrical charge. However, the solutions obtained when we consider the gauge sector with CPT-even and parity-odd coe cients have non-zero electric eld. The implementation of the BPS formalism provides self-dual equations whose solutions have total energy proportional to the magnetic ux. We have studied in detail the axially symmetrical v ortices-like solutions using the appropriate ansatz. We note that the magnetic ux as well as being proportional to the winding number, also depends on the CPT-even coe cients of the Higgs sector. We show that there exist a sets of valuesfor the CPT-even coe cients of Higgs sector that reproduce the con gurations for the abelian Higgs models already studied in literature. Another important result is the existence of a set of parameters involving only the CPT-even case, in which the BPS (Bogomoln'yi-Prasad-Sommer eld) v ortices exhibit localized inversion of both magnetic and electric eld. In the second chapter, still in the context of Lorentz invariance symmetry violation, we study the self-dual con gurations in the O (3) nonlinear sigma model coupled to a gauge eld. The usual model is modi ed by introducing the CPT-odd term of CFJ in the gauge sector and a CPT-even term in the sigma sector, both modifying only the kinetic sectors. The con gurations have non-null total charge and are proportional to the magnetic ux. The BPS formalism provides the self-dual equations with con gurations having total energy proportional to the topological charge of the model. Then we study the axially symmetric v ortices solutions. These have total energy proportional to the winding number and depends on the Lorentz violation coe cients belonging to the sigma sector. This dependence is re ected in the topological charge and in the magnetic ux. Similarly to the previous case, there exist a set of values for the CPTeven coe cients of the sigma sector that interpolate the con gurations of usual O (3) nonlinear sigma models coupled to a gauge eld already found in literature. On the third and nal part of this manuscript we study the existence of self-dual con - gurations in models for abelian Higgs generalized models: Maxwell-Higgs, Born-Infeld-Higgs, Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs. The generalization modi es the kinetics of the elds by means of functions that depend only on the Higgs eld ( ). During the development of the implementation of the BPS formalism, naturally arises the explicit function that generalize the kinetic term of the Higgs eld, j j2 􀀀2; > 1. Thus, we are able to determined the self-dual potential and the corresponding rst order equations for each model. Among the self-dual con gurations, we study the vortex-like solutions and found that from a given value of the parameter the pro les begin to acquire a shape similar to the form of compactons-like solutions.