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<p>We investigate whether the effective theory for isolated, massive, and weakly interacting spin-3<i>/</i>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 <i>S</i>-matrix consistency conditions for the longitudinal and transverse polarizations of massive spin-3<i>/</i>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 <i>t</i>–<i>u</i> 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.</p>

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(Super) gravity from positivity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Brando Bellazzini,
  • Alex Pomarol,
  • Marcello Romano,
  • Francesco Sciotti

摘要

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.