Defeitos topológicos: propriedades e aplicações

Abstract

In this work some intrinsic phenomena of Theories of Strings and Membranes are investigated. We use results of Gauge Theories and the study of the properties of topological field theories in several dimensions. Membranes are simulate by domain walls in several dimensions, while-the fundamental string it can be seen as a tube of magnetic flux propagating in the space. This is only possible due to certain existent analogies among the solitons of the gauge theory and the fundamental objects of the theory of strings. First, it is studied the appearance of topological terms in membranes in several di?mensions in abelian and non-abelian field theories. The fundamental point for this study is a generalization for higher dimensions of the anomalous interaction between the axion and the photon in D = 4 (which is a topological term), in the abelian case. In the non?-abelian case, it is studied a version of the term θ of QCD in dimensions D > 4. Models of this type present the so called Peccei-Quinn symmetry, associated to the resolution of the problem of non-conservation of the symmetry CP in QCD. This symmetry, when broken, it can originate solitonic stable states that will be identified as the membranes of the theory. In this case we start from a theory written in D = 6 and, by dimensional reductions, we arrive in a theory in D = 3. In all these cases, well-known topological terms (Chern-Simons, B Ʌ F) appear on the membranes which appear in the models. An interesting aspect found it is that the constants of the topological terms are quantized on the membranes. As an application of the previous study, we consider an explicit localization mechanism of topological gravity in membranes. We obtain, starting from a non-abelian theory in D = 5, an effective topological term on the membrane, which can be classified as B Ʌ F type. This term can be used, if properly parametrized, in order to describe gravitational degrees of freedom. In fact, the gravity can be described by a Yang-Mills gauge field theory, where the fundamental quantities of the theory are denominated tetrads. In this sense, e used a parametrization already introduced in the literature. Using Kalb-Ramond tensorial fields (represented by B), we built a topological term Chern-Simons-like in D = 5 and we showed that this interaction type generates mass for the fiel B. This was made in order to study the anisotropic mass generation mechanism for this field in the presence of a tachyon condensates. The interaction of the condensate with the tensorial field is obtained through a topological term that generalizes for D = 6 the anomalous interaction between the axion and the photon. In spite of the theory to be indeed written in D = 5, it is observed that, due to the existence of the condensate, the tensorial field will still possess vibrational modes in D = 6. As another application, we studied mechanisms of location of gauge fields in membranes through systems in field theories that support topological defects inside of defects. It as know that the more appropriate mechanism , which do not have charge universality problems, consists of a cosmic string (open string), which carries confined magnetic field flux in the phase of Higgs, with a point tied up to a domain wall (membrane), where the magnetic flux becomes deconfined, or in other words, it enters in the Coulomb phase. This model includes only one real scalar field and one complex scalar field, besides one vectorial gauge e field. It can be shown that this system is stable by calculation of the Bogomolnyi limit. We studied systems involving a larger content of complex fields. In a simpler case, the increment of one complex scalar field can result in a condensate on the membrane that can generate a flow tube in its interior, depending on the potential that describes the interactions in this system. In other words, the gauge field would be located in the membrane of a different way from the discussed one.