Old and New No Go Theorems on Interacting Massless Particles in Flat Space

TL;DR

The paper surveys model-independent no-go results for massless high-spin interactions with gravity in flat space, emphasizing Weinberg's soft-limit argument and the Weinberg–Witten extension. It shows that, when combined, these theorems confine long-range couplings to spins $s \le 2$ and imply a unique massless graviton, ruling out consistent interactions for $s>2$ with gravity. The work analyzes a proposed counterexample based on AdS/Vasiliev constructions with an RS2 cutoff, demonstrating that boundary terms spoil gauge invariance unless a mass is generated for the high-spin field. It also discusses a nonlocal higher-spin proposal, noting potential issues with locality, unitarity, and causality, highlighting the robustness of the no-go conclusions for local theories.

Abstract

We review model independent arguments showing that massless particles interacting with gravity in a Minkowski background space can have at most spin two. These arguments include a classic theorem due to Weinberg, as well as a more recent extension of the Weinberg-Witten theorem. A puzzle arising from an apparent counterexample to these theorems is examined and resolved.

Figures (3)

• Figure 1: Factorization of S-matrix amplitude in the soft limit
• Figure 2: A singular vertex implies the existence of an additional massless particle mixing with the graviton.
• Figure 3: "Exotic" particles cannot interact at all with gravity.