(Super) gravity from positivity

A bstract We investigate whether the effective theory for isolated, massive, and weakly interacting spin-3 / 2 particles is compatible with causality and unitarity — i.e., the positivity of scattering amplitudes. We find no solution to positivity constraints, except when gravitons are also present and couple in a (nearly) supersymmetric way. Gravity is thus bootstrapped from S -matrix consistency conditions for the longitudinal and transverse polarizations of massive spin-3 / 2 states. For two such particles forming a U(1)-charged state, a (gravi)photon gauging the symmetry is also required, with couplings characteristic of supergravity and consistent with both the no-global-symmetry and weak gravity conjectures. We further explore the EFT-hedron associated with the longitudinal polarizations, the Goldstinos, through novel t – u symmetric dispersion relations. We identify the ‘extremal’ UV models that lie at the corners of the allowed parameter space, recovering familiar models of supersymmetry breaking and uncovering new ones.