Partial Masslessness of Higher Spins in (A)dS

TL;DR

This paper explores the phenomenon of partial masslessness in higher spin fields within (A)dS backgrounds, revealing new gauge invariances and analyzing their unitarity and degrees of freedom across different spins.

Contribution

It introduces a comprehensive analysis of partial masslessness for higher spins, deriving gauge invariances, unitarity conditions, and extending wave operators to half-integer spins.

Findings

Partial masslessness occurs along specific lines in (m^2, Λ) space.

Only spin 3 models are unitary among those studied.

Higher spins exhibit gauge invariances and degree of freedom counts consistent with partial masslessness.

Abstract

Massive spin s>=3/2 fields can become partially massless in cosmological backgrounds. In the plane spanned by m^2 and \Lambda, 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,\Lambda) 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.