Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions

TL;DR

This paper explores the duality between a self-dual non-gauge invariant theory and a topologically massive $B $ theory in 3+1 dimensions, analyzing their classical and quantum equivalences through the master action method and matter coupling.

Contribution

It demonstrates the duality between the two theories using the master action approach and extends the duality to include matter fields with a Thirring-like interaction.

Findings

Duality holds at classical level with matching degrees of freedom.

The master action explicitly interpolates between the theories.

Duality persists at quantum level with effective Lagrangians.

Abstract

In this work, we revisit the duality between a self-dual non-gauge invariant theory and a topological massive theory in $3+1$ dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is build using a $B \wedge F$ term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we employ the master action method to obtain a fundamental Lagrangian that interpolates between these two theories and makes evident the role of the topological $B \wedge F$ term in the duality relation. By coupling these theories with matter fields, we show that the duality holds provided a Thirring-like term is included. In addition, we use the master action in order to probe the duality upon the quantized fields. We carried out a functional integration of the fields and compared the resulting effective Lagrangians.