Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Carrollian Holographic Duals Are Nonlocal

Jordan Cotler1,*, Prateksh Dhivakar2,†, and Kristan Jensen2,‡

  • *Contact author: jcotler@fas.harvard.edu
  • †Contact author: pratekshd@uvic.ca
  • ‡Contact author: kristanj@uvic.ca

Phys. Rev. Lett. 137, 091601 – Published 25 August, 2026

DOI: https://doi.org/10.1103/f26s-4p77

Abstract

Mapping the S matrix of a generic theory of flat-space gravity coupled to matter to correlation functions of a putative Carrollian dual, we show that bulk interactions imply boundary nonlocality.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (86)

  1. G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Classical Quantum Gravity 24, F15 (2007).
  2. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062.
  3. A. Bagchi, Correspondence between asymptotically flat spacetimes and nonrelativistic conformal field theories, Phys. Rev. Lett. 105, 171601 (2010).
  4. C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Classical Quantum Gravity 31, 092001 (2014).
  5. A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards flatspace holography from non-relativistic symmetries, J. High Energy Phys. 10 (2012) 092.
  6. A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, Flat holography: Aspects of the dual field theory, J. High Energy Phys. 12 (2016) 147.
  7. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
  8. S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81, 1062 (2021).
  9. A.-M. Raclariu, Lectures on celestial holography, arXiv:2107.02075.
  10. A. Bagchi, A. Banerjee, P. Dhivakar, S. Mondal, and A. Shukla, The Carrollian kaleidoscope, Eur. Phys. J. C 86, 429 (2026).
  11. S. B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61, 106008 (2000).
  12. M. Gary, S. B. Giddings, and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80, 085005 (2009).
  13. J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, J. High Energy Phys. 03 (2011) 025.
  14. A. L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, J. High Energy Phys. 10 (2012) 127.
  15. S. Raju, New recursion relations and a flat space limit for AdS/CFT correlators, Phys. Rev. D 85, 126009 (2012).
  16. E. Hijano, Flat space physics from AdS/CFT, J. High Energy Phys. 07 (2019) 132.
  17. A. Bagchi, P. Dhivakar, and S. Dutta, AdS Witten diagrams to Carrollian correlators, J. High Energy Phys. 04 (2023) 135.
  18. L. F. Alday, M. Nocchi, R. Ruzziconi, and A. Yelleshpur Srikant, Carrollian amplitudes from holographic correlators, J. High Energy Phys. 03 (2025) 158.
  19. A. Lipstein, R. Ruzziconi, and A. Yelleshpur Srikant, Towards a flat space Carrollian hologram from AdS4/CFT3, J. High Energy Phys. 06 (2025) 073.
  20. G. Arenas-Henriquez, L. Ciambelli, F. Diaz, W. Jia, and D. Rivera-Betancour, Radiation in fluid/gravity and the flat limit, J. High Energy Phys. 01 (2026) 086.
  21. R. Basu and U. N. Chowdhury, Dynamical structure of Carrollian electrodynamics, J. High Energy Phys. 04 (2018) 111.
  22. A. Bagchi, A. Mehra, and P. Nandi, Field theories with conformal Carrollian symmetry, J. High Energy Phys. 05 (2019) 108.
  23. A. Bagchi, R. Basu, A. Mehra, and P. Nandi, Field theories on null manifolds, J. High Energy Phys. 02 (2020) 141.
  24. K. Banerjee, R. Basu, A. Mehra, A. Mohan, and A. Sharma, Interacting conformal Carrollian theories: Cues from electrodynamics, Phys. Rev. D 103, 105001 (2021).
  25. M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, J. High Energy Phys. 11 (2021) 180.
  26. B. Chen, R. Liu, and Y.-f. Zheng, On higher-dimensional Carrollian and Galilean conformal field theories, SciPost Phys. 14, 088 (2023).
  27. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll symmetry, dark energy and inflation, Front. Phys. 10, 810405 (2022).
  28. P.-x. Hao, W. Song, X. Xie, and Y. Zhong, BMS-invariant free scalar model, Phys. Rev. D 105, 125005 (2022).
  29. E. Bergshoeff, J. Figueroa-O’Farrill, and J. Gomis, A non-lorentzian primer, SciPost Phys. Lect. Notes 69, 1 (2023).
  30. A. Bagchi, A. Banerjee, S. Dutta, K. S. Kolekar, and P. Sharma, Carroll covariant scalar fields in two dimensions, J. High Energy Phys. 01 (2023) 072.
  31. A. Saha, Intrinsic approach to 1+1D Carrollian conformal field theory, J. High Energy Phys. 12 (2022) 133.
  32. W.-B. Liu and J. Long, Symmetry group at future null infinity: Scalar theory, Phys. Rev. D 107, 126002 (2023).
  33. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll stories, J. High Energy Phys. 09 (2023) 148.
  34. K. Banerjee, R. Basu, B. Krishnan, S. Maulik, A. Mehra, and A. Ray, One-loop quantum effects in Carroll scalars, Phys. Rev. D 108, 085022 (2023).
  35. F. Ecker, D. Grumiller, M. Henneaux, and P. Salgado-Rebolledo, Carroll swiftons, Phys. Rev. D 110, L041901 (2024).
  36. J. Cotler, K. Jensen, S. Prohazka, A. Raz, M. Riegler, and J. Salzer, Quantizing Carrollian field theories, J. High Energy Phys. 10 (2024) 049.
  37. J. Cotler, K. Jensen, S. Prohazka, M. Riegler, and J. Salzer, Soft gravitons in three dimensions, J. High Energy Phys. 07 (2025) 002.
  38. A. Sharma, Studies on Carrollian quantum field theories, Classical Quantum Gravity 43, 045006 (2026).
  39. J. Cotler, P. Dhivakar, and K. Jensen, A finite Carrollian critical point, J. High Energy Phys. 08 (2025) 172.
  40. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  41. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107, 126027 (2023).
  42. A. Bagchi, P. Dhivakar, and S. Dutta, Holography in flat spacetimes: The case for Carroll, J. High Energy Phys. 08 (2024) 144.
  43. P. Kraus and R. M. Myers, Carrollian partition functions and the flat limit of AdS, J. High Energy Phys. 01 (2025) 183.
  44. D. Jain, S. Kundu, S. Minwalla, O. Parrikar, S. G. Prabhu, and P. Shrivastava, The S-matrix and boundary correlators in flat space, J. High Energy Phys. 02 (2026) 151.
  45. S. Banerjee, S. Ghosh, and R. Gonzo, BMS symmetry of celestial OPE, J. High Energy Phys. 04 (2020) 130.
  46. K. Nguyen and J. Salzer, Operator product expansion in Carrollian CFT, J. High Energy Phys. 07 (2025) 193.
  47. M. Guica, T. Hartman, W. Song, and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80, 124008 (2009).
  48. M. Guica, K. Skenderis, M. Taylor, and B. C. van Rees, Holography for Schrodinger backgrounds, J. High Energy Phys. 02 (2011) 056.
  49. W. Song and A. Strominger, Warped AdS3/Dipole-CFT Duality, J. High Energy Phys. 05 (2012) 120.
  50. R. Haag and D. Kastler, An Algebraic approach to quantum field theory, J. Math. Phys. (N.Y.) 5, 848 (1964).
  51. L. Freidel, D. Pranzetti, and A.-M. Raclariu, Sub-subleading soft graviton theorem from asymptotic Einstein’s equations, J. High Energy Phys. 05 (2022) 186.
  52. A. Ball, Celestial locality and the Jacobi identity, J. High Energy Phys. 01 (2023) 146.
  53. S. Banerjee and S. Pasterski, Revisiting the shadow stress tensor in celestial CFT, J. High Energy Phys. 04 (2023) 118.
  54. A. Fiorucci, D. Grumiller, and R. Ruzziconi, Logarithmic celestial conformal field theory, Phys. Rev. D 109, L021902 (2024).
  55. See Supplemental Material at http://link.aps.org/supplemental/10.1103/f26s-4p77 where we relegated a few technical asides concerning locality and Carrollian physics, including a discussion of the quantization of local Carrollian “field theory” and complications that arise in attempting to match entanglement measures obtained from flat space gravity to a local Carrollian dual, which includes Refs. [56–59].
  56. A. Bagchi, R. Basu, D. Grumiller, and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114, 111602 (2015).
  57. H. Jiang, W. Song, and Q. Wen, Entanglement entropy in flat holography, J. High Energy Phys. 07 (2017) 142.
  58. L. Apolo, H. Jiang, W. Song, and Y. Zhong, Modular Hamiltonians in flat holography and (W)AdS/WCFT, J. High Energy Phys. 09 (2020) 033.
  59. L. Apolo, H. Jiang, W. Song, and Y. Zhong, Swing surfaces and holographic entanglement beyond AdS/CFT, J. High Energy Phys. 12 (2020) 064.
  60. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  61. S. Pasterski, S.-H. Shao, and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96, 065026 (2017).
  62. S. Banerjee, Null infinity and unitary representation of the poincare group, J. High Energy Phys. 01 (2019) 205.
  63. S. Banerjee, S. Ghosh, P. Pandey, and A. P. Saha, Modified celestial amplitude in Einstein gravity, J. High Energy Phys. 03 (2020) 125.
  64. J. Kulp and S. Pasterski, Multiparticle states for the flat hologram, J. High Energy Phys. 08 (2025) 091.
  65. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  66. R. K. Sachs, Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-time, Proc. R. Soc. A 270, 103 (1962).
  67. S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017).
  68. Only the combinations aout…aoutain†…ain† contribute inside S-matrix elements; terms with aout† on the left or ain on the right annihilate the in and out vacua and drop out prior to the Mellin transform.

  69. Appendix A in [41] contains the map needed to work entirely at ℐ+.

  70. We follow the standard notation where boldface symbols of the form pi are used to denote vectors in 3D space, whereas four momenta are denoted by pi.

  71. S^ is the evolution operator generated by the interaction picture Hamiltonian.

  72. I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, Holography from conformal field theory, J. High Energy Phys. 10 (2009) 079.
  73. S. Banerjee and R. Basu, Light and shadow OPEs: A Carroll symmetric approach to flat holography, J. High Energy Phys. 04 (2026) 176.
  74. L. Mason, R. Ruzziconi, and A. Yelleshpur Srikant, Carrollian amplitudes and celestial symmetries, J. High Energy Phys. 05 (2024) 012.
  75. S. Pasterski, S.-H. Shao, and A. Strominger, Gluon amplitudes as 2D conformal correlators, Phys. Rev. D 96, 085006 (2017).
  76. A. L. Fitzpatrick and J. Kaplan, Scattering states in AdS/CFT, arXiv:1104.2597.
  77. E. Hijano and D. Neuenfeld, Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT, J. High Energy Phys. 11 (2020) 009.
  78. Y.-Z. Li, Notes on flat-space limit of AdS/CFT, J. High Energy Phys. 09 (2021) 027.
  79. A. Fontanella and O. Payne, A Carroll limit of AdS/CFT: A triality with flat space holography?, Phys. Lett. B 879, 140669 (2026).
  80. L. P. de Gioia and A.-M. Raclariu, Celestial sector in CFT: Conformally soft symmetries, SciPost Phys. 17, 002 (2024).
  81. V. Balasubramanian, S. B. Giddings, and A. E. Lawrence, What do CFTs tell us about Anti-de Sitter space-times?, J. High Energy Phys. 03 (1999) 001.
  82. S. B. Giddings, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett. 83, 2707 (1999).
  83. A. L. Fitzpatrick, E. Katz, D. Poland, and D. Simmons-Duffin, Effective conformal theory and the flat-space limit of AdS, J. High Energy Phys. 07 (2011) 023.
  84. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  85. R. Ruzziconi and A. Saha, Holographic Carrollian currents for massless scattering, J. High Energy Phys. 01 (2025) 169.
  86. To keep the notation compact, we do not substitute the parametrization of the momenta pi from (2).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation