On the dual equivalence of the self-dual and topologically massive $B\wedge F$ models coupled to dynamical fermionic matter

TL;DR

This paper demonstrates the duality between self-dual and topologically massive $B ext{-}F$ models with dynamical fermionic matter, revealing how gauge embedding naturally produces the necessary current interactions.

Contribution

It provides a systematic gauge embedding approach to establish the duality, including matter couplings and current interactions, between the two models.

Findings

Duality between $SD_{B ext{-}F}$ and $TM_{B ext{-}F}$ models confirmed.

Gauge embedding naturally generates current-current interaction terms.

Minimal coupling transforms into non-minimal magnetic-like coupling in dual models.

Abstract

We study the equivalence between the $B\wedge F$ self-dual ($SD_{B\wedge F}$) and the $B\wedge F$ topologically massive ($TM_{B\wedge F}$) models including the coupling to dynamical, U(1) charged fermionic matter. This is done through an iterative procedure of gauge embedding that produces the dual mapping. In the interactive cases, the minimal coupling adopted for both vector and tensor fields in the self-dual representation is transformed into a non minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. We show that both terms arise naturally from the embedding procedure.