On the dual equivalence of the self-dual and topologically massive p-form models

TL;DR

This paper demonstrates the duality between self-dual and topologically massive p-form models with a generalized B_q∧F_{p+1} term, using gauge embedding and analyzing matter couplings across arbitrary dimensions.

Contribution

It establishes the duality between self-dual and topologically massive p-form models with matter coupling via a gauge embedding approach, including the natural emergence of current-current interactions.

Findings

Duality between SD_{B∧F} and TM_{B∧F} models proven.

Minimal coupling transforms into a magnetic-like non-minimal coupling.

Current-current interaction terms naturally arise from the embedding.

Abstract

We study the duality symmetry in p-form models containing a generalized $B_q\wedge F_{p+1}$ term in spacetime manifolds of arbitrary dimensions. The equivalence between the $B_q\wedge F_{p+1}$ self-dual ($SD_{B\wedge F}$) and the $B_q\wedge F_{p+1}$ topologically massive ($TM_{B\wedge F}$) models is established using a gauge embedding procedure, including the minimal coupling to conserved charged matter current. The minimal coupling adopted for both 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 adopted. Comparison with Higgs/Julia-Toulouse duality is established.