A note on spin-s duality

TL;DR

The paper develops a unified framework for duality of massless higher-spin bosonic fields using a common first-order parent action inspired by Vasiliev. In $D=4$ the dual description maps to the same Pauli-Fierz/Fronsdal action, revealing a self-dual structure, while in $D=5$ spin-2 duality connects Pauli-Fierz to Curtright. For arbitrary spin $s$, the dual field acquires a mixed Young symmetry of type $(D-3,1,\dots,1)$, and the authors provide explicit dual actions and gauge symmetries obtained by a systematic reduction from the first-order formulation. The approach generalizes spin-2 and spin-3 dualities to all spins via a sequence: trading $B$ for $Y$, solving constraints, irreducible decomposition, and epsilon-duality to a $T$-field; the results unify on-shell and action-level dualities and point to interesting but delicate issues for interactions.

Abstract

Duality is investigated for higher spin ($s \geq 2$), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D=4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s=2) or Fronsdal ($s \geq 3$) action (as it is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev.