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 higher-spin fields with $s\leq3$ in (A)dS propagate on the light cone and, assuming this extends to all $s$, derives the precise $m^2$–$\Lambda$ tunings for higher-spin partial masslessness. It then shows that the unitary region for massive spins shrinks toward $\Lambda=0$ as the spin increases, implying an infinite tower of massive states forces $\Lambda$ to vanish in the high-spin limit. The work further discusses potential relevance to string theory and cosmological supergravity in constant-curvature backgrounds, tying together representation theory, gauge invariance, and the cosmological-constant problem. Overall, it links null propagation to the structure of (A)dS higher-spin representations and explores deep cosmological consequences.

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 Λ=0, so that an infinite tower of massive particles forces vanishing Λ. We also speculate on the relevance of this result to string theory and supergravity in (A)dS backgrounds.