Researchers at IPhT (CEA, CNRS) and the Universitat Autònoma de Barcelona have shown that gravity — and with it, supersymmetry — emerge as logical necessities whenever a massive spin-3/2 particle exists in nature. Two principles are enough: causality, the fact that no signal can travel faster than light, and unitarity, the requirement that probabilities are conserved in quantum mechanics. The structure of supergravity is not assumed: it bootstraps itself.
Crédit : B. Bellazzini, A. Pomarol, M. Romano, F. Sciotti (image générée par IA, annotée par les auteurs).
In fundamental physics, gravity is usually thought of as an ingredient one adds to a theory. But could it instead be forcedby the internal consistency of the quantum world? This is what this study, published in the Journal of High Energy Physics, demonstrates.
The starting point is disarmingly simple: a single massive spin-3/2 particle. The authors show that such a particle simply cannot exist in isolation within a consistent theory. Its scattering amplitudes grow too fast with energy, clashing with positivity inequalities — the mathematical encoding of causality (the speed of light as an absolute limit) and unitarity (the conservation of probabilities in every quantum process). The theory breaks down barely above the particle’s own mass.
Can it be saved by adding other particles — scalars, vector bosons? No: every attempt fails. The contributions systematically carry the wrong sign. There is only one way out: the graviton, the particle of gravity. And it cannot couple just any way: the constraints fix its interactions uniquely, reproducing exactly the structure of supergravity.
Supersymmetry is therefore not a postulate: it is a logical necessity . Famous relations between the gravitino mass, the Planck mass, and the supersymmetry-breaking scale emerge here from the sole demand that probabilities be positive and effects propagate within the light cone. When the particle carries electric charge, the same logic demands that the charge be gauged, fixes the gyromagnetic factor to g = 2, and saturates the Weak Gravity Conjecture — results long conjectured within the Swampland program that here appear as simple corollaries of positivity.