Abstract
We find a model-independent upper bound on the strong coupling scale for a massive spin-2 particle coupled to Einstein gravity. Our approach is to directly construct tree-level scattering amplitudes for these degrees of freedom and use them to find the maximum scale of perturbative unitarity violation. The highest scale is $\Lambda_3=\left(m^2M_P\right)^{1/3}$, which is saturated by ghost-free bigravity. The strong coupling scale can be further raised to $M_P$ if the kinetic term for one particle has the wrong sign, which uniquely gives the amplitudes of quadratic curvature gravity. We also discuss the generalization to massive higher-spin particles coupled to gravity.
Highlights
Every particle that interacts with Einstein gravity in flat spacetime must do so through a minimal coupling vertex with a universal gravitational strength [1]
We present our result for a bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle and discuss several examples of theories subject to this result
III, we find that the highest strong coupling scale in a parity-conserving, unitary effective field theory (EFT) describing a massive spin-2 particle coupled to gravity is
Summary
Every particle that interacts with Einstein gravity in flat spacetime must do so through a minimal coupling vertex with a universal gravitational strength [1]. This property results in powerful constraints on the allowed particles and interactions that can exist alongside Einstein gravity One notable such constraint is that in flat spacetime there can be no local theories of massless higher-spin particles interacting with anything that interacts with Einstein gravity—the required gravitational minimal coupling interactions are incompatible with higher-spin gauge invariance [2,3,4,5].1. This implies that massive higher-spin states cannot exist as isolated elementary particles in flat spacetime all the way up to the Planck scale—they are always accompanied by other particles or strong coupling effects that come in at a lower scale, as in perturbative string theory and confining gauge theories We can understand this quantitatively by determining the maximum Λk for a given spectrum of particles.
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