Universal Limits on Massless High-Spin Particles

TL;DR

The paper shows that massless high-spin particles with spin $s>2$ cannot couple to gravity in flat Minkowski space under a broad, model-independent framework. It extends the Weinberg-Witten no-go by weakening gauge-invariance requirements and using an on-shell S-matrix approach with spurious polarizations, deriving a decoupling constraint that cannot be satisfied for $s>2$ while preserving universal gravitational interaction. Separate analyses for fermions and bosons establish a fermionic bound at $s>3/2$ and a bosonic bound at $s\ge3$, effectively excluding massless high-spin states from conventional gravitational coupling in Minkowski space and highlighting the role of the equivalence principle. The work also discusses Abelian gauge coupling constraints, potential loopholes (e.g., massive gravity, AdS), and implications for the viability and realization of higher-spin theories in different spacetime contexts.

Abstract

We present a model-independent argument showing that massless particles interacting with gravity in a Minkowski background space can have at most spin two. This result is proven by extending a famous theorem due to Weinberg and Witten to theories that do not possess a gauge-invariant stress-energy tensor.