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

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.