A Bound on Massive Higher Spin Particles

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.

52 pages + appendices, 7 figures; minor changes, conclusions unchanged

References in corpus (57)

• A bound on chaos
• Causality, Analyticity and an IR Obstruction to UV Completion
• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Conformal Four Point Functions and the Operator Product Expansion
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• The Pomeron and Gauge/String Duality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Projectors, Shadows, and Conformal Blocks
• Conformal Regge theory
• Partial Masslessness of Higher Spins in (A)dS
• Cubic interaction vertices for massive and massless higher spin fields
• Neutrino Physics from the Cosmic Microwave Background and Large Scale Structure
• A Natural Language for AdS/CFT Correlators
• Theorems on gravitational time delay and related issues
• Emergent Spacetime and Holographic CFTs
• Light-ray operators in conformal field theory
• Averaged Null Energy Condition from Causality
• Causality Constraints in Conformal Field Theory
• Non-Gaussianity as a Particle Detector
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• String Lessons for Higher-Spin Interactions
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Effective Conformal Theory and the Flat-Space Limit of AdS
• A Stereoscopic Look into the Bulk
• Higher Spin Gauge Theories in Various Dimensions
• Analyticity and the Holographic S-Matrix
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• A Proof of the Conformal Collider Bounds
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Entanglement, Holography and Causal Diamonds
• Einstein gravity 3-point functions from conformal field theory
• AdS Field Theory from Conformal Field Theory
• Universal Limits on Massless High-Spin Particles
• Bounds for OPE coefficients on the Regge trajectory
• Consistent couplings between spin-2 and spin-3 massless fields
• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
• More Holography from Conformal Field Theory
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• A New Spin on Causality Constraints
• Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields
• A Conformal Collider for Holographic CFTs
• Massive and Massless Spin-2 Scattering and Asymptotic Superluminality
• Massive Spin-5/2 Fields Coupled to Gravity: Tree-Level Unitarity vs. the Equivalence Principle
• Unitarity and positivity constraints for CFT at large central charge
• Causality Constraints on Massive Gravity
• Causality in 3D Massive Gravity Theories
• A Universal Bound on the Strong Coupling Scale of a Gravitationally Coupled Massive Spin-2 Particle
• Eikonal Scattering and Asymptotic Superluminality of Massless Higher Spin Fields

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