A note on spin-s duality

TL;DR

This paper explores duality in higher-spin free massless bosonic fields, deriving dual formulations from a common first-order action and revealing their equivalence to known actions in specific dimensions.

Contribution

It introduces a unified first-order framework for higher-spin dualities, extending previous equation-level analyses to a Lagrangian level, and relates different dual actions in specific dimensions.

Findings

Dual formulations derived from a common parent action.

In D=4, dual theories match original actions for all spins.

In D=5, Pauli-Fierz and Curtright actions are dual.

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.