Manifest Duality Invariance for the Partially Massless Graviton

TL;DR

The paper develops a Maxwell-like duality for the partially massless graviton on de Sitter space, showing that a gauge-invariant field strength $F_{\mu\nu|\lambda}$ and its dual $\tilde F_{\mu\nu|\lambda}$ satisfy a duality-covariant first-order system that interchanges field equations and Bianchi identities. By constructing a $d_L$-based Bianchi structure and a cohomology-consistent complex, it demonstrates that the PM dynamics can be recast in a duality-invariant form with $\mathrm{Tr}\,F=0$ and $d_L\tilde F=0$ alongside their duals, and that this matches the original PM equations when $F$ is expressed as $F=dh$. The work further provides a $3+1$ decomposition in $d=3$ that reveals Maxwell-like dynamics with spatial fields $E_i$, $B_i$, $H_{ij}$, and $K_{ij}$, related by a duality that rotates these pairs and yields four propagating degrees of freedom. Finally, it discusses how sources modify the duality structure and how a magnetic source $\tilde T$ could restore duality in the presence of matter, while noting the challenges of incorporating such sources locally in the free action. This framework clarifies the EM-like character of partially massless gravity and paves the way for consistent non-linear extensions involving dual sources.

Abstract

For a special value of the mass, a massive graviton on de Sitter space acquires an enhanced scalar gauge symmetry, and is called partially massless. The partially massless graviton possesses a duality invariance akin to electromagnetic duality. We display this duality in its manifestly local and covariant form, in which it acts to interchange the first order field equations and Bianchi identities of a gauge invariant field strength.