Vórtices não-abelianos com acoplamento não-mínimo em um background gravitacional

Abstract

The main purpose of this thesis is to investigate how the non-Abelian gauge symmetry affects the solutions of the equations of motion in some field theory models. We concern ourselves specifically with three dimensional field theories. We will note here that planar systems give us the needed informations about the theories approached here. Topological defects were studied with special attention to the vortex solutions. We will do a general survey on physical symmetries, concerning mainly with the non-abelian symmetry. After describing in a particular view the Yang-Mills theory we will review mainly the models in which vortex solutions appear. For example the abelian Maxwell- Higgs model and the Chern-Simons-Higgs model. The next step is to include the Anomalous Magnetic Dipole Moment(AMDM) with the so called non-minimal coupling. A deeper study envisaging how to implement the non-minimal coupling in a Yang-Mills theory is made. New results were found about the addition of a gravitational background in some of the models cited above. We will also study non minimal coupling and non-abelian symmetry in this gravitational background.