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Infinite-dimensional symmetries in plane wave spacetimes

Emilie Despontin*, Stéphane Detournay†, and Dima Fontaine‡

  • *Contact author: emilie.despontin@ulb.be
  • †Contact author: sdetourn@ulb.ac.be
  • ‡Contact author: dima.fontaine@ulb.be
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Phys. Rev. D 113, 106003 – Published 6 May, 2026

DOI: https://doi.org/10.1103/2q94-5crl

Abstract

We study the asymptotic symmetries of the Nappi-Witten spacetime in four dimensions, a plane wave arising as the Penrose limit of AdS2×S2. Imposing suitable boundary conditions at large transverse distance, we uncover a new infinite-dimensional symmetry algebra allowing for nontrivial central extensions. The corresponding phase space encompasses the most general four-dimensional pp-wave metric, including in particular the Penrose limit of Kerr black holes.

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References (52)

  1. M. Blau, Plane waves and penrose limits, Lecture Notes for the ICTP School on Mathematics in String and Field Theory (2003) (2011).
  2. D. Marolf and S. F. Ross, Plane waves: To infinity and beyond!, Classical Quantum Gravity 19, 6289 (2002).
  3. V. E. Hubeny and M. Rangamani, No horizons in pp-waves, J. High Energy Phys. 11 (2002) 021.
  4. R. Güven, Plane wave limits and t-duality, Phys. Lett. B 482, 255 (2000).
  5. G. T. Horowitz and A. R. Steif, Strings in strong gravitational fields, Phys. Rev. D 42, 1950 (1990).
  6. G. T. Horowitz and A. A. Tseytlin, Exact solutions and singularities in string theory, Phys. Rev. D 50, 5204 (1994).
  7. R. Metsaev, Type IIB Green–Schwarz superstring in plane wave Ramond–Ramond background, Nucl. Phys. B625, 70 (2002).
  8. R. Metsaev and A. A. Tseytlin, Exactly solvable model of superstring in plane wave ramond-ramond background, Phys. Rev. D 65, 126004 (2002).
  9. D. E. Berenstein, J. M. Maldacena, and H. S. Nastase, Strings in flat space and pp waves from N=4 superYang-Mills, J. High Energy Phys. 04 (2002) 013.
  10. D. Sadri and M. Sheikh-Jabbari, The plane-wave/super Yang-Mills duality, Rev. Mod. Phys. 76, 853 (2004).
  11. J. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38, 1113 (1999).
  12. S. Gubser, I. Klebanov, and A. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428, 105 (1998).
  13. E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  14. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rep. 323, 183 (2000).
  15. A. Strominger, Black hole entropy from near-horizon microstates, J. High Energy Phys. 02 (1998) 009.
  16. S. Carlip, Black hole entropy from conformal field theory in any dimension, Phys. Rev. Lett. 82, 2828 (1999).
  17. M. Cvetič and F. Larsen, Near horizon geometry of rotating black holes in five dimensions, Nucl. Phys. B531, 239 (1998).
  18. S. Carlip, Near-horizon conformal symmetry and black hole entropy, Phys. Rev. Lett. 88, 241301 (2002).
  19. M. Guica, T. Hartman, W. Song, and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80, 124008 (2009).
  20. S. E. Gralla, A. Lupsasca, and D. P. Marrone, The shape of the black hole photon ring: A precise test of strong-field general relativity, Phys. Rev. D 102, 124004 (2020).
  21. S. Hadar, D. Kapec, A. Lupsasca, and A. Strominger, Holography of the photon ring, Classical Quantum Gravity 39, 215001 (2022).
  22. K. Fransen, Quasinormal modes from penrose limits, Classical Quantum Gravity 40, 205004 (2023).
  23. D. Kapec and A. Sheta, pp-waves and the hidden symmetries of black hole quasinormal modes, Classical Quantum Gravity 42, 155002 (2025).
  24. C. R. Nappi and E. Witten, Wess-Zumino-Witten model based on a nonsemisimple group, Phys. Rev. Lett. 71, 3751 (1993).
  25. A. Strominger, AdS(2) quantum gravity and string theory, J. High Energy Phys. 01 (1999) 007.
  26. G. Barnich and C. Troessaert, BMS charge algebra, J. High Energy Phys. 12 (2011) 105.
  27. C. Duval, G. Gibbons, P. Horvathy, and P. Zhang, Carroll symmetry of plane gravitational waves, Classical Quantum Gravity 34, 175003 (2017).
  28. H. Afshar, X. Bekaert, and M. Najafizadeh, Classification of conformal carroll algebras, J. High Energy Phys. 12 (2024) 148.
  29. L. Ciambelli and L. Lehner, Fluid-gravity correspondence and causal first-order relativistic viscous hydrodynamics, Phys. Rev. D 108, 126019 (2023).
  30. L. Freidel and D. Pranzetti, Gravity from symmetry: Duality and impulsive waves, J. High Energy Phys. 04 (2022) 125.
  31. L. Ciambelli, From asymptotic symmetries to the corner proposal, Proc. Sci., Modave2022 (2023) 002 [arXiv:2212.13644].
  32. R. Penrose, Any space-time has a plane wave as a limit, in Differential Geometry and Relativity: A Volume in Honour of André Lichnerowicz on His 60th Birthday (Springer, New York, 1976), pp. 271–275.
  33. M. Blau, J. Figueroa-O’Farrill, and G. Papadopoulos, Penrose limits, supergravity and brane dynamics, Classical Quantum Gravity 19, 4753 (2002).
  34. C. Duval, G. W. Gibbons, P. A. Horvathy, and P.-M. Zhang, Carroll symmetry of plane gravitational waves, Classical Quantum Gravity 34, 175003 (2017).
  35. E. Despontin, S. Detournay, S. Dutta, and D. Fontaine, Anisotropic conformal Carroll field theories and their gravity duals, J. High Energy Phys. 09 (2025) 056.
  36. S. Deser and R. Jackiw, Three-dimensional cosmological gravity: Dynamics of constant curvature, Ann. Phys. (N.Y.) 153, 405 (1984).
  37. J. D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity, Commun. Math. Phys. 104, 207 (1986).
  38. V. Iyer and R. M. Wald, Some properties of the noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50, 846 (1994).
  39. G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B633, 3 (2002).
  40. G. Compère, Note on the first law with p-form potentials, Phys. Rev. D 75, 124020 (2007).
  41. S. Detournay and M. Guica, Stringy Schrödinger truncations, J. High Energy Phys. 08 (2013) 121.
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/2q94-5crl for Mathematica file.
  43. J. Bosma, M. Geiller, S. Majumdar, and B. Oblak, Radiative asymptotic symmetries of 3D Einstein-Maxwell theory, SciPost Phys. 16, 092 (2024).
  44. L. Freidel, A canonical bracket for open gravitational system, arXiv:2111.14747.
  45. L. Freidel and D. Pranzetti, The extended corner symmetry algebra of 4d gravity, J. High Energy Phys. 04 (2021) 135.
  46. L. Ciambelli, From asymptotic symmetries to the corner proposal, Proc. Sci., Modave2022 (2023) 002 [arXiv:2212.13644].
  47. H. Adami, M. M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo, and C. Zwikel, Symmetries at null boundaries: Two and three dimensional gravity cases, J. High Energy Phys. 10 (2020) 107.
  48. M. Geiller, C. Goeller, and C. Zwikel, 3d gravity in Bondi-Weyl gauge: Charges, corners, and integrability, J. High Energy Phys. 09 (2021) 029.
  49. L. Ciambelli, A. Delfante, R. Ruzziconi, and C. Zwikel, Symmetries and charges in Weyl-Fefferman-Graham gauge, Phys. Rev. D 108, 126003 (2023).
  50. L. Ciambelli, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Fefferman-Graham and Bondi gauges in the fluid/gravity correspondence, Proc. Sci., CORFU2019 (2020) 154 [arXiv:2006.10083].
  51. E. G. Gimon, A. Hashimoto, O. Lunin, V. E. Hubeny, and M. Rangamani, Black strings in asymptotically plane wave geometries, J. High Energy Phys. 08 (2003) 035.
  52. J. Ben Achour and J.-P. Uzan, Displacement versus velocity memory effects from a gravitational plane wave, J. Cosmol. Astropart. Phys. 08 (2024) 004.

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Phys. Rev. D 113, 106003– Published 6 May, 2026
  • Received 1 September 2025
  • Accepted 16 March 2026
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