Condições de consistência para localização de campos

Abstract

In this thesis, we study the consistency of the localization of the scalar, spinor and abelian vector fields in brane models. In the context of extra dimensions, the so-called braneworlds play an important role. These models are premised on the possibility of describing our universe (4D) as a hypersurface (brane) in a higher dimensional spacetime (bulk). In addition, it is required that the gravitational and matter fields are confined on the brane, in order to reproduce the known results. In general, confinement consists of factoring the action of the fields on the bulk into an effective action on the brane and an integral on the extra dimensions K. From this, we say that the effective theory on the brane is well-defined (localized) on the brane when the integral in the extra dimensions is finite. This procedure, when applied to fields of matter, does not consider the possible effects of these fields on the metric. This is exactly the point that we address in this thesis. Based on the assumption that Einstein's equation must be satisfied, we obtained two conditions that the energy-momentum tensor of the fields of matter must obey in order for their confinement to be consistent. With these conditions, we tested the consistency for the scalar (free), spinorial (free and interacting) and abelian vector (free and interacting) fields in several braneworlds found in the literature. For the free vector field we obtained a very interesting result. The zero-mode localization, even with the K integral finite in some 6D models, is not consistent with Einstein's equations. This indicates, therefore, that the effects of this field on the metric cannot be ignored. Furthermore, it indicates that the finite integral argument is not sufficient to ensure a consistent localization. To conclude, we discussed the possibility of confining fields by arguments of symmetry. Exploring the Hodge duality symmetry for free p-form fields, we show that it is possible to infer the localization of other fields.