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Planck mass gravitinos in Einstein-Maxwell backgrounds

Artur Krawczyk1, Krzysztof A. Meissner1, Hermann Nicolai2, and Bartłomiej Sikorski1

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Phys. Rev. D 114, 045013 – Published 18 August, 2026

DOI: https://doi.org/10.1103/qpnl-91n5

Abstract

Charged massive spin-3/2 fields have long been regarded as problematic, because their coupling to electromagnetism generically leads to loss of hyperbolicity, acausal propagation and loss of unitarity. At the same time, fractionally charged supermassive gravitinos play a central role in a recent proposal of two of the present authors, where they are the only fermionic degrees of freedom beyond the Standard Model and provide novel dark matter candidates. We address this apparent tension by revisiting the result of Deser and Waldron, who showed that the inclusion of gravity can compensate the electromagnetic source of the inconsistency. For a minimally coupled Rarita-Schwinger field in an Einstein-Maxwell background, consistency requires a lower bound on the mass in terms of the charge and the cosmological constant. What is usually a severe obstruction to low-energy charged spin-3/2 phenomenology becomes an independent indication that such particles must lie close to the Planck scale, as argued by two of the present authors on other grounds. We rederive the inequality from the solvability of the Rarita-Schwinger constraints and from the characteristic determinant, emphasizing how the Einstein-Maxwell stress tensor compensates the purely electromagnetic pathology. We then reformulate the system using a Stückelberg spinor, showing that the helicity-1/2 sector reproduces the same condition. This formulation is also essential for obtaining a renormalizable propagator. We discuss this propagator and the corresponding ghost system.

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References (39)

  1. K. Johnson and E. C. G. Sudarshan, Inconsistency of the local field theory of charged spin 3/2 particles, Ann. Phys. (N.Y.) 13, 126 (1961).
  2. G. Velo and D. Zwanziger, Propagation and quantization of Rarita-Schwinger waves in an external electromagnetic potential, Phys. Rev. 186, 1337 (1969).
  3. J. Madore and W. Tait, Propagation of shock waves in interacting higher spin wave equations, Commun. Math. Phys. 30, 201 (1973).
  4. J. A. Madore, The characteristic surface of a classical spin-3/2 field in an Einstein-Maxwell background, Phys. Lett. 55B, 217 (1975).
  5. G. W. Gibbons, A note on the Rarita-Schwinger equation in a gravitational background, J. Phys. A 9, 145 (1976).
  6. S. Deser, V. Pascalutsa, and A. Waldron, Massive spin 3/2 electrodynamics, Phys. Rev. D 62, 105031 (2000).
  7. S. Deser and A. Waldron, Inconsistencies of massive charged gravitating higher spins, Nucl. Phys. B631, 369 (2002).
  8. M. Porrati and R. Rahman, Causal propagation of a charged spin 3/2 field in an external electromagnetic background, Phys. Rev. D 80, 025009 (2009).
  9. R. Rahman, Helicity-1/2 mode as a probe of interactions of a massive Rarita-Schwinger field, Phys. Rev. D 87, 065030 (2013).
  10. K. Benakli, The two lives of a massive charged spin-32 particle: From superstrings EFT to supergravity, J. High Energy Phys. 06 (2026) 117.
  11. S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. 62B, 335 (1976).
  12. S. Deser and B. Zumino, Broken supersymmetry and supergravity, Phys. Rev. Lett. 38, 1433 (1977).
  13. K. A. Meissner and H. Nicolai, Supermassive gravitinos and giant primordial black holes, Phys. Rev. D 102, 103008 (2020).
  14. K. A. Meissner and H. Nicolai, Origin and growth of primordial black holes, Phys. Lett. B 819, 136468 (2021).
  15. S. Ask, A Review of the supersymmetry searches at LEP, in 38th Rencontres de Moriond on Electroweak Interactions and Unified Theories (2003), .
  16. X. Portell Bueso, Supersymmetry searches at the Tevatron and the LHC collider experiments, in 31st International Symposium on Physics in Collision (2011), arXiv:1112.1723.
  17. S. Sekmen, Supersymmetry searches in CMS run 2: A complete review, Highlights High-Energy Phys. 1, 18 (2025).
  18. K. A. Meissner and H. Nicolai, Standard model fermions and infinite-dimensional R-symmetries, Phys. Rev. Lett. 121, 091601 (2018).
  19. K. A. Meissner and H. Nicolai, Standard model symmetries and K(E10), J. High Energy Phys. 08 (2025) 054.
  20. M. Gell-Mann, From renormalizability to calculability?, in Shelter Island II: Proceedings of the 1983 Shelter Island Conference on Quantum Field Theory and the Fundamental Problems of Physics, edited by R. Jackiw, N. N. Khuri, S. Weinberg, and E. Witten (The MIT Press, Cambridge, MA, 1985), pp. 3–23.
  21. T. Damour, M. Henneaux, and H. Nicolai, E(10) and a ’small tension expansion’ of M theory, Phys. Rev. Lett. 89, 221601 (2002).
  22. K. A. Meissner and H. Nicolai, Standard Model fermions and N=8 supergravity, Phys. Rev. D 91, 065029 (2015).
  23. A. Kleinschmidt and H. Nicolai, Standard model fermions and K (E10), Phys. Lett. B 747, 251 (2015).
  24. A. Kleinschmidt and H. Nicolai, E(10) cosmology, J. High Energy Phys. 01 (2006) 137.
  25. K. A. Meissner and H. Nicolai, Planck mass charged gravitino dark matter, Phys. Rev. D 100, 035001 (2019).
  26. S. D. McDermott, H.-B. Yu, and K. M. Zurek, Turning off the lights: How dark is dark matter?, Phys. Rev. D 83, 063509 (2011).
  27. A. D. Dolgov, S. L. Dubovsky, G. I. Rubtsov, and I. I. Tkachev, Constraints on millicharged particles from Planck data, Phys. Rev. D 88, 117701 (2013).
  28. E. Del Nobile, M. Nardecchia, and P. Panci, Millicharge or decay: A critical take on minimal dark matter, J. Cosmol. Astropart. Phys. 04 (2016) 048.
  29. A. H. Guth, D. I. Kaiser, and Y. Nomura, Inflationary paradigm after Planck 2013, Phys. Lett. B 733, 112 (2014).
  30. Y. Akrami et al., Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  31. S. Deser and A. Waldron, Gauge invariances and phases of massive higher spins in (A)dS, Phys. Rev. Lett. 87, 031601 (2001).
  32. A. K. Das and D. Z. Freedman, Gauge quantization for spin 3/2 fields, Nucl. Phys. B114, 271 (1976).
  33. D. Z. Freedman and A. K. Das, Gauge internal symmetry in extended supergravity, Nucl. Phys. B120, 221 (1977).
  34. S. Deser and A. Waldron, (Dis)continuities of massless limits in spin 3/2 mediated interactions and cosmological supergravity, Phys. Lett. B 501, 134 (2001).
  35. M. J. Duff, J. T. Liu, and H. Sati, Quantum discontinuity for massive spin 3/2 with a Lambda term, Nucl. Phys. B680, 117 (2004).
  36. G. F. Sterman, P. K. Townsend, and P. van Nieuwenhuizen, Unitarity, Ward identities, and new quantization rules of supergravity, Phys. Rev. D 17, 1501 (1978).
  37. R. Endo and M. Takao, Feynman gauge for Rarita-Schwinger field in higher dimensions and chiral U(1) anomaly, Phys. Lett. B 161, 155 (1985).
  38. N. K. Nielsen, Ghost counting in supergravity, Nucl. Phys. B140, 499 (1978).
  39. R. E. Kallosh, Modified Feynman rules in supergravity, Nucl. Phys. B141, 141 (1978).

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Phys. Rev. D 114, 045013– Published 18 August, 2026
  • Received 24 June 2026
  • Accepted 14 July 2026
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