Manifest Duality for Partially Massless Higher Spins

TL;DR

This work develops a covariant, gauge-invariant curvature framework for partially massless higher-spin fields in $D=4$, unifying PM fields across all spins $s$ and depths $t$ through a Maxwell-like set of equations on a curvature ${\cal K}$. A nilpotent differential complex $d^{(s,t)}_i$ ties the gauge parameters, potentials, field strengths, and Bianchi identities, enabling recovery of the PM equations via curvature constraints and gauge fixing; in $D=4$ a simple duality $\delta {\cal K} = *{\cal K}$ exchanges equations and Bianchi identities, revealing an EM-like structure across depths. The paper provides explicit treatment for depths $t=0,1$ and sketches the general $t\ge 2$ case, including detailed spin-3 examples, $d+1$ decompositions, and residual gauge symmetries, thereby clarifying the role of duality and paving the way for actions and nonlinear extensions. These results offer a structured path toward covariant actions, potential non-Abelian generalizations, and connections to frame-like higher-spin formalisms, with implications for PM dynamics in (A)dS backgrounds and beyond.

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.

Figures (1)

• Figure 1: Partially massless lines and regions for spin 3. Modes pass between being healthy and ghostlike as the partially massless lines are crossed.