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  • Letter
  • Open Access

New higher-spin curvatures in flat space

Nicolas Boulanger*, Andrea Campoleoni†, and Simon Pekar‡

  • Service de Physique de l’Univers, Champs et Gravitation, Université de Mons—UMONS, 20 place du Parc, 7000 Mons, Belgium

  • *nicolas.boulanger@umons.ac.be
  • †andrea.campoleoni@umons.ac.be
  • ‡simon.pekar@umons.ac.be Present address: Centre de Physique Théorique – CPHT, École polytechnique, Unité Mixte de Recherche 7644 du CNRS, Institut Polytechnique de Paris, 91120 Palaiseau Cedex, France.
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Phys. Rev. D 108, L101904 – Published 28 November, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L101904

Abstract

It was shown that the Lie algebra underlying higher-spin holography admits a contraction including a Poincaré subalgebra in any space-time dimensions. The associated curvatures, however, do not reproduce upon linearization those that are usually employed to formulate the equations of motion of free massless particles in Minkowski space. We show that, despite this mismatch, the new linearized curvatures can also be used to describe massless higher-spin fields. This suggests a new way to build interacting higher-spin gauge theories in Minkowski space that may admit a holographic description.

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References (55)

  1. X. Bekaert, N. Boulanger, and P. Sundell, How higher-spin gravity surpasses the spin two barrier: No-go theorems versus yes-go examples, Rev. Mod. Phys. 84, 987 (2012).
  2. A. Sagnotti, Notes on strings and higher spins, J. Phys. A 46, 214006 (2013).
  3. S. Giombi, Higher spin—CFT duality, in New Frontiers in Fields and Strings (World Scientific, Singapore, 2017), pp. 137–214, https://www.worldscientific.com/doi/abs/10.1142/9789813149441_0003.
  4. X. Bekaert, N. Boulanger, A. Campoleoni, M. Chiodaroli, D. Francia, M. Grigoriev et al., Snowmass White Paper: Higher spin gravity and higher spin symmetry, in Snowmass 2021 (2022), .
  5. M. A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243, 378 (1990).
  6. M. A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567, 139 (2003).
  7. E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B644, 303 (2002).
  8. I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550, 213 (2002).
  9. E. S. Fradkin and M. A. Vasiliev, Candidate to the role of higher spin symmetry, Ann. Phys. (N.Y.) 177, 63 (1987).
  10. N. Boulanger, D. Ponomarev, E. D. Skvortsov, and M. Taronna, On the uniqueness of higher-spin symmetries in AdS and CFT, Int. J. Mod. Phys. A 28, 1350162 (2013).
  11. S. E. Konstein and M. A. Vasiliev, Extended higher spin superalgebras and their massless representations, Nucl. Phys. B331, 475 (1990).
  12. M. A. Vasiliev, Higher spin superalgebras in any dimension and their representations, J. High Energy Phys. 12 (2004) 046.
  13. E. Sezgin and P. Sundell, Supersymmetric higher spin theories, J. Phys. A 46, 214022 (2013).
  14. X. Bekaert, S. Cnockaert, C. Iazeolla, and M. A. Vasiliev, Nonlinear higher spin theories in various dimensions, in Proceedings of the 1st Solvay Workshop on Higher Spin Gauge Theories (2004), pp. 132–197, arXiv:hep-th/0503128.
  15. V. E. Didenko and E. D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975.
  16. V. E. Lopatin and M. A. Vasiliev, Free Massless Bosonic Fields of Arbitrary Spin in d-dimensional De Sitter Space, Mod. Phys. Lett. A 03, 257 (1988).
  17. C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18, 3624 (1978).
  18. E. Joung and M. Taronna, Cubic-interaction-induced deformations of higher-spin symmetries, J. High Energy Phys. 03 (2014) 103.
  19. S. Weinberg, Photons and gravitons in s-matrix theory: Derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135, B1049 (1964).
  20. M. Porrati, Universal limits on massless high-spin particles, Phys. Rev. D 78, 065016 (2008).
  21. N. Boulanger, S. Leclercq, and P. Sundell, On the uniqueness of minimal coupling in higher-spin gauge theory, J. High Energy Phys. 08 (2008) 056.
  22. X. Bekaert, N. Boulanger, and S. Leclercq, Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex, J. Phys. A 43, 185401 (2010).
  23. D. Ponomarev and E. D. Skvortsov, Light-Front Higher-Spin Theories in Flat Space, J. Phys. A 50, 095401 (2017).
  24. K. Krasnov, E. Skvortsov, and T. Tran, Actions for self-dual higher spin gravities, J. High Energy Phys. 08 (2021) 076.
  25. L. Ren, M. Spradlin, A. Yelleshpur Srikant, and A. Volovich, On effective field theories with celestial duals, J. High Energy Phys. 08 (2022) 251.
  26. D. Ponomarev, Towards higher-spin holography in flat space, J. High Energy Phys. 01 (2023) 084.
  27. R. Monteiro, From Moyal deformations to chiral higher-spin theories and to celestial algebras, J. High Energy Phys. 03 (2023) 062.
  28. A. Campoleoni and S. Pekar, Carrollian and Galilean conformal higher-spin algebras in any dimensions, J. High Energy Phys. 02 (2022) 150.
  29. X. Bekaert, A. Campoleoni, and S. Pekar, Carrollian conformal scalar as flat-space singleton, Phys. Lett. B 838, 137734 (2023).
  30. A. A. Sharapov and E. D. Skvortsov, Formal higher-spin theories and Kontsevich–Shoikhet–Tsygan formality, Nucl. Phys. B921, 538 (2017).
  31. A. Sharapov and E. Skvortsov, Formal higher spin gravities, Nucl. Phys. B941, 838 (2019).
  32. A. G. Nikitin, Generalized killing tensors of arbitrary rank and order, Ukrainian Mathematical Journal 43, 734 (1991).
  33. M. G. Eastwood, Higher symmetries of the Laplacian, Ann. Math. 161, 1645 (2005).
  34. X. Bekaert, E. Joung, and J. Mourad, Comments on higher-spin holography, Fortschr. Phys. 60, 882 (2012).
  35. J. de Boer and S. N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B665, 545 (2003).
  36. G. Arcioni and C. Dappiaggi, Holography in asymptotically flat space-times and the BMS group, Classical Quantum Gravity 21, 5655 (2004).
  37. L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, Flat holography and Carrollian fluids, J. High Energy Phys. 07 (2018) 165.
  38. S. Pasterski, M. Pate, and A.-M. Raclariu, Celestial holography, in Snowmass 2021 (2022), .
  39. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  40. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  41. E. D. Skvortsov, Mixed-symmetry massless fields in Minkowski space unfolded, J. High Energy Phys. 07 (2008) 004.
  42. E. D. Skvortsov, Frame-like actions for massless mixed-symmetry fields in Minkowski space, Nucl. Phys. B808, 569 (2009).
  43. N. Boulanger, C. Iazeolla, and P. Sundell, Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism, J. High Energy Phys. 07 (2009) 013.
  44. C. Iazeolla and P. Sundell, A fiber approach to harmonic analysis of unfolded higher-spin field equations, J. High Energy Phys. 10 (2008) 022.
  45. N. Boulanger and E. D. Skvortsov, Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime, J. High Energy Phys. 09 (2011) 063.
  46. E. Joung and K. Mkrtchyan, Notes on higher-spin algebras: Minimal representations and structure constants, J. High Energy Phys. 05 (2014) 103.
  47. M. P. Blencowe, A consistent interacting massless higher spin field theory in D=(2+1), Classical Quantum Gravity 6, 443 (1989).
  48. H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller, and J. Rosseel, Spin-3 gravity in three-dimensional flat space, Phys. Rev. Lett. 111, 121603 (2013).
  49. H. A. Gonzalez, J. Matulich, M. Pino, and R. Troncoso, Asymptotically flat spacetimes in three-dimensional higher spin gravity, J. High Energy Phys. 09 (2013) 016.
  50. M. Ammon, D. Grumiller, S. Prohazka, M. Riegler, and R. Wutte, Higher-spin flat space cosmologies with soft hair, J. High Energy Phys. 05 (2017) 031.
  51. M. Ammon, M. Pannier, and M. Riegler, Scalar fields in 3D asymptotically flat higher-spin gravity, J. Phys. A 54, 105401 (2021).
  52. R. R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B759, 147 (2006).
  53. E. S. Fradkin and M. A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189, 89 (1987).
  54. A. Saha, Carrollian approach to 1+3D flat holography, J. High Energy Phys. 06 (2023) 051.
  55. D. Grumiller and W. Merbis, Near horizon dynamics of three dimensional black holes, SciPost Phys. 8, 010 (2020).

Outline

Information

Phys. Rev. D 108, L101904– Published 28 November, 2023
  • Received 15 June 2023
  • Accepted 13 October 2023
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