Positivity in Massive Spin-3/2 EFTs and the Planck-Suppressed Neighbourhood of Supergravity
Abstract
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 π©=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 βͺ MPl, the volume of the allowed region scales parametrically as Vol βΌ m6/MPl6 , and shrinks to zero as m β 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.
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BibTeX
@misc{desai2026positivity,
title = {{Positivity in Massive Spin-3/2 EFTs and the Planck-Suppressed Neighbourhood of Supergravity}},
author = {Jay Desai and Diptimoy Ghosh and Saurabh Pant},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.11072},
eprint = {2605.11072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11072},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Positivity in Massive Spin-3/2 EFTs and the Planck-Suppressed Neighbourhood of Supergravity
AU - Jay Desai
AU - Diptimoy Ghosh
AU - Saurabh Pant
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2605.11072
UR - https://arxiv.org/abs/2605.11072
AB - 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 π©=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 βͺ M_Pl, the volume of the allowed region scales parametrically as Vol βΌ m^6/M_Pl^6 , and shrinks to zero as m β 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.
ER -