Campos tensoriais de matéria abelianos e não-abelianos: geração de massa e dualidade

Abstract

In this Thesis we analyze the generation of mass to the antisymmetric tensor matter field Tµν in a non-Abelian model and the mapping of the antisymmetric matter field to the antisymmetric tensor gauge field Bµν in the Abelian case. For the mass generation, we use two different mechanisms. The first one is the spontaneous symmetry breaking, where we use scalar fields with nonzero expected vacuum value in the SU(N) representation. Besides the massive term for the matter field, by relaxing the requirement of parity invariance we obtain topological terms such as eTµνTµν. The second mechanism is denominated topological mass generation. It consists by introducing in the action of a vectorial complex field and a massive topological coupling term between Bµν and complex selfdual field. Direct calculation of the Feynman propagators show us that the matter field has a massive pole. In dual mapping, we can say that the U(1) invariant action of the matter field is mapped in a dual action described by the antisymmetric tensor gauge field Bµν and a topologically conserved current. Two remarkable characteristics can be observed in this mapping: the first one is the parity preservation due to topological terms in the both dual actions; the second characteristic is that, though the conserved current admits topological terms, the mapping is free of axial anomalies. The presence of anomalies prevents the conservation of topological currents in a mapping such as bosonization in 4 dimensions. In that case, anomalies are present due to the γ 5 matrix. One of the most important requisites for the renormalizability of a theory in all orders of ¯h is that the theory must be free of anomalies.