Closed strings and weak gravity from higher-spin causality

We combine old and new quantum field theoretic arguments to show that any theory of stable or metastable higher spin particles can be coupled gravity only when the sector has a stringy structure. Metastable particles, free interacting, cannot couple while preserving causality unless there exist states in gravitational much below Planck scale $M_{\rm pl}$. obtain an upper bound on mass $\Lambda_{\rm gr}$ lightest particle terms quantities non-gravitational sector. invoke CKSZ uniqueness theorem argue weakly UV completion such must have containing infinite towers asymptotically parallel, equispaced, linear Regge trajectories. Consequently, four-point scattering amplitudes coincide with closed string amplitude for $s,t\gg1$, identifying as scale. Our also implies all 4d masses $m\ll \Lambda_{\rm satisfy weak condition.