Relation between standard and exotic duals of differential forms

TL;DR

This paper investigates the relationship between standard and exotic dualities of differential forms, demonstrating their algebraic equivalence as free fields and exploring their implications for gauge theories and higher duals.

Contribution

It establishes that exotic duals are algebraically related to standard duals, showing their equivalence for free fields and extending the relation to higher mixed symmetry duals.

Findings

Exotic duals are algebraically related to standard duals.

Standard and exotic duals provide equivalent descriptions for free fields.

The relation extends to higher mixed symmetry duals.

Abstract

Exotic duality suggests a link between gauge theories for differential p-forms and tensor fields of mixed symmetry [D-2,p] in D spacetime dimensions. On the other hand, standard Hodge duality relates p-form to (D-p-2)-form gauge potentials by exchanging their field equations and Bianchi identities. Following the methodology and the recent proposal of Henneaux, Lekeu and Leonard that the double dual of the free graviton is algebraically related to the original graviton and does not provide a new, independent description of the gravitational field, we examine the status of exotic duality for p-forms. We find that the exotic dual is algebraically related to the standard dual of a differential form and therefore they provide equivalent descriptions as free fields. Introducing sources then leads to currents being proportional. This relation is extended in a straightforward way for higher exotic duals of the mixed symmetry type [D-2,...,D-2,p].