Positivity in massive spin-3/2 EFTs and the Planck-suppressed neighbourhood of supergravity

A bstract It is well known that a strictly massless spin-3/2 particle can interact consistently only within supergravity. Recently, positivity arguments have shown that an effective field theory of a massive Majorana spin-3/2 particle admits an arbitrarily small mass only if a graviton is present and the four-fermion contact interactions are tuned to the values dictated by N N = 1 supergravity. In this work, we investigate how this limit is approached at finite mass. Assuming that the graviton t -channel pole can be discarded, we derive non-forward, tree-level dispersive bounds on massive spin-3/2 contact operators and determine the region of effective couplings consistent with unitarity and analyticity. For sufficiently small m , we find that the allowed parameter space forms a bounded, Planck-suppressed neighbourhood of the supergravity point, defined by the supergravity values of the four-fermion couplings. The supergravity point lies on the boundary of this region. In the regime m ≪ M Pl , the volume of the allowed region scales parametrically as Vol~ m⁶MPl⁶, Vol ~ m 6 M Pl 6 , and shrinks to zero as m → 0, smoothly reproducing the massless-limit results. The allowed region becomes unbounded when mass approaches the Planck scale. We further analyze the effect of including additional light scalar and pseudo-scalar degrees of freedom, motivated by the Polonyi model, and find that their couplings are also bounded in a way similar to the contact couplings and that it doesn’t enlarge the allowed contact coupling space.