A Bound on Massive Higher Spin Particles

TL;DR

The authors prove a universal bound ruling out a finite number of massive higher-spin particles (J>2) from causally coupling to gravitons in flat and AdS spacetimes with Einstein-Hilbert gravity. They employ flat-space eikonal scattering to derive positivity constraints on J−J−graviton vertices and extend the analysis to AdS via the holographic null energy condition, showing that any finite tower is incompatible with causality. The only way to preserve causality is to introduce an infinite tower of higher-spin states whose masses are near the lightest particle and which can decay into gravitons, effectively lowering the gravitational EFT cutoff. In cosmology, these bounds constrain higher-spin signatures during inflation, predicting exponential suppression in the squeezed limit unless a string-like spectrum with Λ∼H is present. Overall, the work connects high-energy consistency conditions to observable consequences in AdS/CFT, flat space, and early-universe phenomenology, highlighting the necessity of an infinite higher-spin tower for causality in theories with gravity.

Abstract

According to common lore, massive elementary higher spin particles lead to inconsistencies when coupled to gravity. However, this scenario was not completely ruled out by previous arguments. In this paper, we show that in a theory where the low energy dynamics of the gravitons are governed by the Einstein-Hilbert action, any finite number of massive elementary particles with spin more than two cannot interact with gravitons, even classically, in a way that preserves causality. This is achieved in flat spacetime by studying eikonal scattering of higher spin particles in more than three spacetime dimensions. Our argument is insensitive to the physics above the effective cut-off scale and closes certain loopholes in previous arguments. Furthermore, it applies to higher spin particles even if they do not contribute to tree-level graviton scattering as a consequence of being charged under a global symmetry such as $\mathbb{Z}_2$. We derive analogous bounds in anti-de Sitter spacetime from analyticity properties of correlators of the dual CFT in the Regge limit. We also argue that an infinite tower of fine-tuned higher spin particles can still be consistent with causality. However, they necessarily affect the dynamics of gravitons at an energy scale comparable to the mass of the lightest higher spin particle. Finally, we apply the bound in de Sitter to impose restrictions on the structure of three-point functions in the squeezed limit of the scalar curvature perturbation produced during inflation.

Figures (7)

• Figure 1: Spectrum of elementary particles with spin $J>2$ in a theory where the dynamics of gravitons is described by the Einstein-Hilbert action at energy scales $E\ll \Lambda$. The cut-off scale $\Lambda$ can be the string scale and hence there can be an infinite tower of higher spin particles above $\Lambda$. Figure (a) represents a scenario that also contains a finite number of higher spin particles below the cut-off and hence violates causality. Causality can only be restored if these particles are accompanied by an infinite tower of higher spin particles with comparable masses which is shown in figure (b). This necessarily brings down the cut-off scale to $\Lambda_{\text{new}}=m$, where $m$ is the mass of the lightest higher spin particle.
• Figure 2: Tree-level exchange diagrams are the building blocks of ladder diagrams.
• Figure 3: Eikonal scattering of particles. In this highly boosted kinematics, particles are moving almost in the null directions such that the center of mass energy is large.
• Figure 4: The three-point interaction between two elementary particles with spin $J$ and a graviton.
• Figure 5: Bounds from interference in $D=4$. In-states are linear combinations of massive higher spin particle $X$ and the graviton $h$.