Formalismo BPS em modelos Baby-Skyrme

Abstract

In this work we present a review on the nonlinear sigma 0 (3) model and the baby Skyrme model, which is a generalization of the first one. In addition, we seek to apply the BPS formalism in models with Skyrmions. We introduce the concept of topological solutions and their connection to the spontaneous breaking of symmetry. Then, we show the Higgs mechanism, which allows mass generation of the gauge particles. Then, we will approach the non-linear sigma model that allows non-trivial field solutions with the introduction of a link in the Lagrangean. We find exact solutions to the model through BPS formalism. Given the problem of the invariance of scale of the solitons, we see that it is possible to break this invariance by adding spin 1 fields together with a suitable potential term, we see that such an addition is quite natural for the description of a realistic system. In that sense, another interesting choice is to consider a Skyrme model. We demonstrate the motivations and applications of a theory with Skyrmions and we see there cent models treated with BPS Formalism. We find the BPS equations of a new Skyrme-Maxwell-Sigma-Model generalized model through a function called textit superpotential. Finally, we investigate the consequences of non-minimally coupling Skyrmions by means of a Pauli term.