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Trivector symmetry of 11-dimensional supergravity

W. H. Baron1,*, D. Marqués2,3,†, C. A. Núñez2,‡, and N. Yazbek4,§

  • *Contact author: wbaron@fisica.unlp.edu.ar
  • †Contact author: diegomarques@iafe.uba.ar
  • ‡Contact author: carmen@iafe.uba.ar
  • §Contact author: nyazbek@dm.uba.ar
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Phys. Rev. D 112, 046008 – Published 8 August, 2025

DOI: https://doi.org/10.1103/3tl6-c4b5

Abstract

Kaluza-Klein reductions of 11-dimensional supergravity lead to exceptional global symmetries in lower dimensions. Certain nongeometric elements of these symmetries, parametrized by a trivector γ, are not inherited from the higher-dimensional local symmetries, but represent instead a symmetry enhancement produced by the isometries of the background. Here, we demonstrate how to realize this enhancement in 11 dimensions, as a symmetry principle with constrained parameters. We show that γ transformations exchange the equations of motion of the metric and the three-form with their Bianchi identities, in a closed form, structuring them into trivector multiplets. Implementing this principle as an off shell symmetry of the theory requires the introduction of a hierarchy of dual fields, including a six-form and a dual graviton in the initial levels.

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References (37)

  1. W. H. Baron, D. Marques, and C. A. Nunez, β symmetry of supergravity, Phys. Rev. Lett. 130, 061601 (2023).
  2. W. H. Baron, D. Marques, and C. A. Nunez, Exploring the β symmetry of supergravity, J. High Energy Phys. 12 (2023) 006.
  3. W. H. Baron and N. A. Yazbek, β symmetry in type II supergravities, J. High Energy Phys. 03 (2024) 146.
  4. W. H. Baron, C. A. Nunez, and J. A. Rodriguez, β symmetry of heterotic supergravity, J. High Energy Phys. 01 (2025) 127.
  5. P. C. West, E11 and M theory, Classical Quantum Gravity 18, 4443 (2001).
  6. F. Riccioni and P. C. West, Dual fields and E11, Phys. Lett. B 645, 286 (2007).
  7. P. West, E11, generalised space-time and IIA string theory, Phys. Lett. B 696, 403 (2011).
  8. A. G. Tumanov and P. West, E11 and the non-linear dual graviton, Phys. Lett. B 779, 479 (2018).
  9. K. Glennon and P. West, The non-linear dual gravity equation of motion in eleven dimensions, Phys. Lett. B 809, 135714 (2020).
  10. G. Dall’Agata, K. Lechner, and D. P. Sorokin, Covariant actions for the bosonic sector of d=10 IIB supergravity, Classical Quantum Gravity 14, L195 (1997).
  11. G. Dall’Agata, K. Lechner, and M. Tonin, D=10, N=IIB supergravity: Lorentz invariant actions and duality, J. High Energy Phys. 07 (1998) 017.
  12. E. Bergshoeff, R. Kallosh, T. Ortin, D. Roest, and A. Van Proeyen, New formulations of D=10 supersymmetry and D8—O8 domain walls, Classical Quantum Gravity 18, 3359 (2001).
  13. I. A. Bandos, A. J. Nurmagambetov, and D. P. Sorokin, Various faces of type IIA supergravity, Nucl. Phys. B676, 189 (2004).
  14. H. Nicolai, P. K. Townsend, and P. van Nieuwenhuizen, Comments on 11-dimensional supergravity, Lett. Nuovo Cimento Soc. Ital. Fis. 30, 315 (1981).
  15. R. D’Auria and P. Fre, Geometric supergravity in d=11 and its hidden supergroup, Nucl. Phys. B201, 101 (1982); B206, 496(E) (1982).
  16. P. K. Townsend and P-Brane Democracy, in Proceedings of 19th Johns Hopkins Workshop and 5th PASCOS Interdisciplinary Symposium, Baltimore, USA, March 22-25, 1995 (1995), pp. 271–285.
  17. P. West, Generalised geometry, eleven dimensions and E11, J. High Energy Phys. 02 (2012) 018.
  18. S. P. de Alwis, Coupling of branes and normalization of effective actions in string/M theory, Phys. Rev. D 56, 7963 (1997).
  19. H. Nishino, Alternative formulation for duality symmetric eleven-dimensional supergravity coupled to super M five-brane, Mod. Phys. Lett. A 14, 977 (1999).
  20. E. A. Bergshoeff, M. de Roo, and O. Hohm, Can dual gravity be reconciled with E11?, Phys. Lett. B 675, 371 (2009).
  21. I. A. Bandos, N. Berkovits, and D. P. Sorokin, Duality symmetric eleven-dimensional supergravity and its coupling to M-branes, Nucl. Phys. B522, 214 (1998).
  22. D. P. Sorokin, The incomprehensible simplicity of PST, arXiv:2501.17918.
  23. T. Curtright, Generalized gauge fields, Phys. Lett. 165B, 304 (1985).
  24. N. Boulanger, P. P. Cook, J. A. O’Connor, and P. West, Higher dualisations of linearised gravity and the A1+++ algebra, J. High Energy Phys. 12 (2022) 152.
  25. C. M. Hull, Strongly coupled gravity and duality, Nucl. Phys. B583, 237 (2000).
  26. C. M. Hull, Duality in gravity and higher spin gauge fields, J. High Energy Phys. 09 (2001) 027.
  27. C. M. Hull, Magnetic charges for the graviton, J. High Energy Phys. 05 (2024) 257.
  28. X. Bekaert, N. Boulanger, and M. Henneaux, Consistent deformations of dual formulations of linearized gravity: A no go result, Phys. Rev. D 67, 044010 (2003).
  29. X. Bekaert, N. Boulanger, and S. Cnockaert, No self-interaction for two-column massless fields, J. Math. Phys. (N.Y.) 46, 012303 (2005).
  30. N. Boulanger and O. Hohm, Non-linear parent action and dual gravity, Phys. Rev. D 78, 064027 (2008).
  31. O. Hohm and H. Samtleben, The dual graviton in duality covariant theories, Fortschr. Phys. 67, 1900021 (2019).
  32. M. Ciafardini, D. Marques, C. A. Núñez, and A. P. Grau, Hidden symmetries from extra dimensions, J. High Energy Phys. 02 (2025) 072.
  33. I. Bakhmatov, N. S. Deger, E. T. Musaev, E. Ó. Colgáin, and M. M. Sheikh-Jabbari, Tri-vector deformations in d=11 supergravity, J. High Energy Phys. 08 (2019) 126.
  34. A. Kulyabin and E. T. Musaev, SUSY and tri-vector deformations, Symmetry 14, 2525 (2022).
  35. I. Bakhmatov, A. Çatal-Özer, N. S. Deger, K. Gubarev, and E. T. Musaev, Generalized 11D supergravity equations from tri-vector deformations, Eur. Phys. J. C 83, 37 (2023).
  36. E. T. Musaev and T. Petrov, Tri-vector deformations on compact isometries, Eur. Phys. J. C 83, 399 (2023).
  37. S. Barakin, K. Gubarev, and E. T. Musaev, Tri-vector deformations with external fluxes, Eur. Phys. J. C 84, 1312 (2024).

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Phys. Rev. D 112, 046008– Published 8 August, 2025
  • Received 23 May 2025
  • Accepted 16 July 2025
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