Abstract
We combine old and new quantum field theoretic arguments to show that any theory of stable or metastable higher spin particles can be coupled to gravity only when the gravity sector has a stringy structure. Metastable higher spin particles, free or interacting, cannot couple to gravity while preserving causality unless there exist higher spin states in the gravitational sector much below the Planck scale Mpl. We obtain an upper bound on the mass Λgr of the lightest higher spin particle in the gravity sector in terms of quantities in the non-gravitational sector. We invoke the CKSZ uniqueness theorem to argue that any weakly coupled UV completion of such a theory must have a gravity sector containing infinite towers of asymptotically parallel, equispaced, and linear Regge trajectories. Consequently, gravitational four-point scattering amplitudes must coincide with the closed string four-point amplitude for s, t ≫ 1, identifying Λgr as the string scale. Our bound also implies that all metastable higher spin particles in 4d with masses m ≪ Λgr must satisfy a weak gravity condition.
Highlights
We combine old and new quantum field theoretic arguments to show that any theory of stable or metastable higher spin particles can be coupled to gravity only when the gravity sector has a stringy structure
A recent bound on the gravitational interactions of massive higher spin (HS) particles [9] implies that a theory with a finite number of elementary massive HS particles cannot be causal unless there exist HS states in the gravity sector much below the Planck scale
In this work we will extend the causality constraints of [9] and combine them with the theorem of CKSZ to argue that when a theory of metastable HS particles is coupled to gravity, a weakly coupled UV completion of the resulting theory must have HS particles in the gravity sector with many of the properties of fundamental strings
Summary
It is our goal to establish that a weak gravity condition and stringy states in the gravity sector emerge naturally when one couples theories of metastable HS particles to gravity. Consider a non-gravitational QFT which may contain both low spin and HS particles {GJ } We assume that this theory has a consistent S-matrix. We assume that the particles {GJ } remain effectively elementary below the energy scale ΛQFT even when we couple the theory to gravity. The S-matrix in the resulting theory still is a meromorphic function with simple poles which are located at the position of {GJ } particles, the graviton hμν, and other particles in the gravity sector (if any). In the limit Mpl → ∞, the tree-level scattering amplitude is a meromorphic function with simple poles only at the location of {GJ } particles. The scattering amplitude may develop additional simple poles which only disappear in the strict limit of Mpl → ∞ These extra poles represent other particles in the gravity sector. We will argue that these additional gravitational poles are essential to the preservation of causality
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