Null Propagation of Partially Massless Higher Spins in (A)dS and Cosmological Constant Speculations

TL;DR

This paper demonstrates that all partially and strictly massless fields with spins up to 3 in (A)dS space propagate null signals, and explores how this constrains the cosmological constant and relates to higher spin theories, string theory, and supergravity.

Contribution

It explicitly proves null propagation for spins s<=3 and hypothesizes this extends to higher spins, deriving conditions linking mass, spin, and the cosmological constant.

Findings

All spins s<=3 in (A)dS propagate null signals.

Higher spin theories impose specific mass-cosmological constant relations.

An infinite tower of massive particles favors a vanishing cosmological constant.

Abstract

We show explicitly that all partially and strictly massless fields with spins s<=3 in (A)dS have null propagation. Assuming that this property holds also for s>3, we derive the mass-cosmological constant tunings required to yield all higher spin partially massless theories. As s increases, the unitarily allowed region for massive spins is squeezed around \Lambda=0, so that an infinite tower of massive particles forces vanishing \Lambda. We also speculate on the relevance of this result to string theory and supergravity in (A)dS backgrounds.