Aspectos da equivalência entre modelos topologicamente massivos com termo B Ʌ F acoplados à matéria em 3+1 dimensões

Abstract

The aim of this work is to revisit some dualities between non-invariant gauge and topologically massive models, in particular a 3 + 1 dimension theory containing the topological term known as B Ʌ F. The lagrangian of the self-dual model in 3 + 1 dimensions consists of a vector field and an antisymmetric field tensor, while the lagrangian of the topologically massive model is constructed using a term B Ʌ F. Although lagrangians are quite different, they have equations of motion that are connected by a simple dual mapping between fields. We discussed this duality by analyzing the degrees of freedom in both theories and comparing their modes of propagation at the classical level. In addition, we use the master action method to obtain a fundamental lagrangian that interpolates between these two theories and makes the role of the topological term B Ʌ F evident in the duality relationship. By coupling these theories to fields of matter, we show that duality remains, as long as a term similar to Thirring’s is included. In addition, we use the master action to test the duality in the quantized fields. We performed a functional integration of the fields and compared the resulting effective lagrangians.