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].
Highlights
Maxwell’s equations in vacuum, or in the presence of both electric and magnetic charges, exhibit a duality in the sense that they may be described in terms of two different gauge potentials
We studied the relation between standard and exotic dual fields of differential forms
Our results indicate that only two dual fields should be thought of as providing inequivalent descriptions of the theory, the rest being connected to them by two towers of algebraic relations
Summary
Maxwell’s equations in vacuum, or in the presence of both electric and magnetic charges, exhibit a duality in the sense that they may be described in terms of two different gauge potentials. The conclusion is that the role of the double dual is different than that of the standard dual field, and its status is not of one providing an independent description of the gravitational field, in the sense that field equations and Bianchi identities are not exchanged in that case This provides additional evidence for the absence of a doubly magnetic source at the level of linearized gravity. It has been argued that, apart from the standard ðD − p − 2Þ-form dual, there exists an infinite number of “exotic” duals [6] These are irreducible mixed-symmetry tensor fields of types 1⁄2D − 2; ...; D − 2; p and 1⁄2D − 2; ...; D − 2; D − p − 2, essentially obtained by appending columns of size D − 2 in the corresponding Young tableaux.
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