Partial Masslessness of Higher Spins in (A)dS
S. Deser, A. Waldron
TL;DR
Deser and Waldron reveal a richer structure for higher spins in (A)dS than in flat space, showing that massive fields can acquire intermediate, partially massless phases along lines in the (m^2, Λ) plane where new gauge invariances appear. They build a unified framework using Bianchi identities, canonical (anti)commutators, and Lichnerowicz-type wave operators to count degrees of freedom and map unitarity regions, illustrating explicit results for s=3/2, s=2, s=5/2, and s=3. Their analysis demonstrates that unitary partially massless theories exist for certain spins in dS (notably s=2 and s=3), while half-integer spins can exhibit nonunitarity on AdS lines, and argues that partial masslessness extends to all higher spins in (A)dS. An Appendix connects the massive higher-spin equations to their massless d=5 Bianchi identities via dimensional reduction, underpinning the dimensional origin of the constraints.
Abstract
Massive spin s>=3/2 fields can become partially massless in cosmological backgrounds. In the plane spanned by m^2 and Λ, there are lines where new gauge invariances permit intermediate sets of higher helicities, rather than the usual flat space extremes of all 2s+1 massive or just 2 massless helicities. These gauge lines divide the (m^2,Λ) plane into unitarily allowed or forbidden intermediate regions where all 2s+1 massive helicities propagate but lower helicity states can have negative norms. We derive these consequences for s=3/2,2 by studying both their canonical (anti)commutators and the transmutation of massive constraints to partially massless Bianchi identities. For s=2, a Hamiltonian analysis exhibits the absence of zero helicity modes in the partially massless sector. For s=5/2,3 we derive Bianchi identities and their accompanying gauge invariances for the various partially massless theories with propagating helicities (+/-5/2,+/-3/2) and (+/-3,+/-2), (+/-3,+/-2,+/-1), respectively. Of these, only the s=3 models are unitary. To these ends, we also provide the half integer generalization of the integer spin wave operators of Lichnerowicz. Partial masslessness applies to all higher spins in (A)dS as seen by their degree of freedom counts. Finally a derivation of massive d=4 constraints by dimensional reduction from their d=5 massless Bianchi identity ancestors is given.