Closed Strings and Weak Gravity from Higher-Spin Causality

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 $M_{\mathrm{pl}}$. We obtain an upper bound on the mass ${\Lambda }_{\mathrm{gr}}$ 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 $s,t\gg 1$, identifying ${\Lambda }_{\mathrm{gr}}$ as the string scale. Our bound also implies that all metastable higher spin particles in 4d with masses $m\ll {\Lambda }_{\mathrm{gr}}$ must satisfy a weak gravity condition.

arXiv comment37 pages + appendices, multiple figures

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