Cite as: doi:10.26081/K61P5Z

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I will show that 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. Causality
imposes an upper bound on the mass of the lightest higher spin particle in the
gravity sector in terms of quantities in the non-gravitational sector. I will
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. This implies that the gravity sector has a stringy
structure with an upper bound on the string scale. Another consequence of this
bound is that all metastable higher spin particles in 4d with masses below the
string scale must satisfy a weak gravity condition. Moreover, these bounds also
have surprising implications for large N QCD coupled to gravity.
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