Null propagation of partially massless higher spins in (A)dS and cosmological constant speculations

We show explicitly that all partially and strictly massless fields with spins s less than or equal to 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 A. We also speculate on the relevance of this result to string theory and supergravity in (A)dS backgrounds. (C) 2001 Published by Elsevier Science B.V.