Manifest Duality for Partially Massless Higher Spins

TL;DR

This paper develops a local, covariant duality-invariant formulation for partially massless fields of all spins and depths in four dimensions, revealing a symmetry akin to electric-magnetic duality.

Contribution

It constructs gauge-invariant curvature tensors for all integer spins and depths, and demonstrates how their equations of motion exhibit duality through first order equations and Bianchi identities.

Findings

Established duality invariance for all spins and depths of partially massless fields.

Provided a covariant, local formulation using curvature tensors.

Revealed the interchange symmetry between equations of motion and Bianchi identities.

Abstract

In four dimensions, partially massless fields of all spins and depths possess a duality invariance akin to electric-magnetic duality. We construct metric-like gauge invariant curvature tensors for partially massless fields of all integer spins and depths, and show how the partially massless equations of motion can be recovered from first order field equations and Bianchi identities for these curvatures. This formulation displays duality in its manifestly local and covariant form, in which it acts to interchange the field equations and Bianchi identities.