Conformal Invariance of Partially Massless Higher Spins

TL;DR

Problem: do conformally invariant theories exist for higher-spin fields in $d=4$ de Sitter beyond Maxwell and spin-2 PM? Approach: classify free higher-spin sectors by depth $t$ in constant-curvature backgrounds and compare the corresponding first-order PM action to the conformally improved scalar action to derive conformal invariance conditions. Result: in $d=4$, maximal-depth PM theories with $t=s$ are conformally invariant, encompassing Maxwell ($s=1$) and PM spin-2 as explicit cases; conformal behavior is supported by lightlike propagation revealed via a Bessel equation with index $\nu = 1/2$. Implications: provides a unified conformal framework for PM higher spins and highlights the remaining challenge of constructing consistent interactions, with possible connections to string-inspired constructions.

Abstract

We show that there exist conformally invariant theories for all spins in d=4 de Sitter space, namely the partially massless models with higher derivative gauge invariance under a scalar gauge parameter. This extends the catalog from the two known gauge models -- Maxwell and partially massless spin 2 -- to all spins.