(Super)$\,$Gravity from Positivity

TL;DR

This paper uses positivity constraints on scattering amplitudes to derive that consistent theories of massive spin-3/2 particles inherently include gravity and supersymmetry, revealing deep connections between these concepts.

Contribution

It demonstrates that positivity constraints enforce the presence of gravity and supersymmetry in theories with massive spin-3/2 particles, and explores the associated EFT-hedron and extremal models.

Findings

Gravity is necessary for consistent spin-3/2 theories.

Supersymmetry emerges as a natural requirement.

New extremal models of supersymmetry breaking are identified.

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.