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arXiv · 2507.12535

(Super)$\,$Gravity from Positivity

Brando Bellazzini·Alex Pomarol·Marcello Romano·Francesco Sciotti
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Abstract

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.

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Brando Bellazzini, Alex Pomarol, Marcello Romano, Francesco Sciotti. 2025-07-16. (Super)$\,$Gravity from Positivity. https://arxiv.org/abs/2507.12535

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