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

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 ∧ 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 ∧ 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.

Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace

“…The fact that there exists a master generating functional (50) which interpolates between (51) and ( 52) is a strong evidence that the duality holds at the quantum level. However, in order to complete the proof of the quantum equivalence between the supersymmetric self-dual and topologically massive models, we need to carry out the remaining integrals in ( 51) and (52).…”

“…Now, let us consider the functional integrals in (52). These integrals are ill-defined due to the gauge invariance of the classical action S T M .…”

“…Analogous to the SD/MCS case in 2 + 1 dimensions, interactions with fermionic fields require Thirring-like terms to preserve the duality mapping. More recently, the proof of duality has been extended to the quantum level through the master action approach and considering arbitrary non-conserved matter currents [52].…”