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In this work, we revisit the duality between a self-dual non-gauge invarianttheory and a topological massive theory in $3+1$ dimensions. The self-dualLagrangian is composed by a vector field and an antisymmetric field tensorwhereas the topological massive Lagrangian is build using a $B \wedge F$ term.Though the Lagrangians are quite different, they yield to equations of motionthat are connected by a simple dual mapping among the fields. We discuss thisduality by analyzing the degrees of freedom in both theories and comparingtheir propagating modes at the classical level. Moreover, we employ the masteraction method to obtain a fundamental Lagrangian that interpolates betweenthese 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, weshow that the duality holds provided a Thirring-like term is included. Inaddition, we use the master action in order to probe the duality upon thequantized fields. We carried out a functional integration of the fields andcompared the resulting effective Lagrangians.

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