Higher spins from exotic dualisations

TL;DR

This paper explores off-shell dualities of massless fields, introducing potentials with extra antisymmetric indices, clarifying degrees of freedom, and applying these ideas to higher spin fields like the double dual graviton and exotic dualities in various dimensions.

Contribution

It provides a detailed analysis of off-shell dualities for massless fields, including the role of extra fields and potentials, and applies these concepts to higher spin and exotic dualities.

Findings

Clarified the counting of degrees of freedom in dual potentials.

Derived action principles for potentials with extra antisymmetric indices.

Applied duality concepts to higher spin fields like the double dual graviton.

Abstract

At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height $h_i$ by columns of height $D-2-h_i$, where $D$ is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of $D-2$ extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in $D=5$ and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in $D=3$.