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  • Open Access

Carrollian amplitudes and holographic correlators in AdS3/CFT2

Iustin Surubaru* and Bin Zhu†

  • School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, EH9 3FD Edinburgh, United Kingdom

  • *Contact author: iustin.surubaru@ed.ac.uk
  • †Contact author: bzhu@ed.ac.uk

Phys. Rev. D 112, 026023 – Published 21 July, 2025

DOI: https://doi.org/10.1103/7t4n-7c6j

Abstract

We study Carrollian amplitudes of massless scalars in (1+2) Minkowski space. Using the prescription recently shown by Alday et al. [Carrollian amplitudes from holographic correlators, J. High Energy Phys. 03 (2025) 158] originally designed for the AdS4 Witten diagrams, we show that AdS3 Witten diagrams in position space in the flat space limit reduce to Carrollian amplitudes. The flat space limit in the bulk is implemented by the Carrollian limit at the boundary. Focusing on four-point correlators with contact and exchange diagrams, we show that the Carrollian limit makes the universality of the bulk point singularity manifest upon performing analytic continuation to the Lorentzian signature of the boundary correlators. Unlike four-point Carrollian amplitudes in (1+3) dimensions, the (1+2) dimensional ones are nondistributional, having analytic properties simpler than the AdS correlators. We also observe for the first time a double copy structure of Carrollian amplitudes.

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References (100)

  1. For recent reviews, see: A. M. Raclariu, Lectures on celestial holography, arXiv:2107.02075; S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81, 1062 (2021); A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448; S. Pasterski, M. Pate, and A. M. Raclariu, Celestial holography, arXiv:2111.11392; L. Donnay, Celestial holography: An asymptotic symmetry perspective, Phys. Rep. 1073, 1 (2024).
  2. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  3. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  4. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107, 126027 (2023).
  5. S. Banerjee, Null infinity and unitary representation of the Poincare group, J. High Energy Phys. 01 (2019) 205.
  6. S. Banerjee, S. Ghosh, P. Pandey, and A. P. Saha, Modified celestial amplitude in Einstein gravity, J. High Energy Phys. 03 (2020) 125.
  7. L. F. Alday, M. Nocchi, R. Ruzziconi, and A. Yelleshpur Srikant, Carrollian amplitudes from holographic correlators, J. High Energy Phys. 03 (2025) 158.
  8. G. Barnich, A. Gomberoff, and H. A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev. D 87, 124032 (2013).
  9. C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Classical Quantum Gravity 31, 092001 (2014).
  10. A. Bagchi, A. Mehra, and P. Nandi, Field theories with conformal Carrollian symmetry, J. High Energy Phys. 05 (2019) 108.
  11. M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, J. High Energy Phys. 11 (2021) 180.
  12. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll symmetry, dark energy and inflation, Front. Phys. 10, 810405 (2022).
  13. B. Chen, R. Liu, H. Sun, and Y. Zheng, Constructing Carrollian field theories from null reduction, J. High Energy Phys. 11 (2023) 170.
  14. J. Salzer, An embedding space approach to Carrollian CFT correlators for flat space holography, J. High Energy Phys. 10 (2023) 084.
  15. A. Saha, w1+∞ and Carrollian holography, J. High Energy Phys. 05 (2024) 145.
  16. K. Nguyen and P. West, Carrollian conformal fields and flat holography, Universe 9, 385 (2023).
  17. K. Nguyen, Carrollian conformal correlators and massless scattering amplitudes, J. High Energy Phys. 01 (2024) 076.
  18. A. Bagchi, P. Dhivakar, and S. Dutta, Holography in flat spacetimes: The case for Carroll, arXiv:2311.11246.
  19. L. Mason, R. Ruzziconi, and A. Yelleshpur Srikant, Carrollian amplitudes and celestial symmetries, arXiv:2312.10138.
  20. W. B. Liu, J. Long, and X. Q. Ye, Feynman rules and loop structure of Carrollian amplitudes, J. High Energy Phys. 05 (2024) 213.
  21. E. Have, K. Nguyen, S. Prohazka, and J. Salzer, Massive Carrollian fields at timelike infinity, J. High Energy Phys. 07 (2024) 054.
  22. S. Stieberger, T. R. Taylor, and B. Zhu, Carrollian amplitudes from strings, J. High Energy Phys. 04 (2024) 127.
  23. T. Adamo, W. Bu, P. Tourkine, and B. Zhu, Eikonal amplitudes on the celestial sphere, J. High Energy Phys. 10 (2024) 192.
  24. S. Banerjee, R. Basu, and S. Atul Bhatkar, Light transformation: A celestial and Carrollian perspective, J. High Energy Phys. 12 (2024) 122.
  25. W. B. Liu, J. Long, H. Y. Xiao, and J. L. Yang, On the definition of Carrollian amplitudes in general dimensions, J. High Energy Phys. 11 (2024) 027.
  26. R. Ruzziconi, S. Stieberger, T. R. Taylor, and B. Zhu, Differential equations for Carrollian amplitudes, J. High Energy Phys. 09 (2024) 149.
  27. R. Ruzziconi and A. Saha, Holographic Carrollian currents for massless scattering, J. High Energy Phys. 01 (2025) 169.
  28. S. Chakrabortty, S. Hegde, and A. Maurya, Differential representation for Carrollian correlators, arXiv:2411.09641.
  29. K. Nguyen and J. Salzer, Operator product expansion in Carrollian CFT, arXiv:2503.15607.
  30. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  31. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  32. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rep. 323, 183 (2000).
  33. L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493, 98 (1999).
  34. J. Polchinski, S matrices from AdS space-time, arXiv:hep-th/9901076.
  35. S. B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61, 106008 (2000).
  36. R. Marotta, K. Skenderis, and M. Verma, Flat space spinning massive amplitudes from momentum space CFT, J. High Energy Phys. 08 (2024) 226.
  37. M. Gary, S. B. Giddings, and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80, 085005 (2009).
  38. J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, J. High Energy Phys. 03 (2011) 025.
  39. A. L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, J. High Energy Phys. 10 (2012) 127.
  40. L. F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, J. High Energy Phys. 12 (2018) 017.
  41. E. Hijano, Flat space physics from AdS/CFT, J. High Energy Phys. 07 (2019) 132.
  42. Y. Z. Li, Notes on flat-space limit of AdS/CFT, J. High Energy Phys. 09 (2021) 027.
  43. H. T. Lam and S. H. Shao, Conformal basis, optical theorem, and the bulk point singularity, Phys. Rev. D 98, 025020 (2018).
  44. L. P. de Gioia and A. M. Raclariu, Eikonal approximation in celestial CFT, J. High Energy Phys. 03 (2023) 030.
  45. L. P. de Gioia and A. M. Raclariu, Celestial amplitudes from conformal correlators with bulk-point kinematics, arXiv:2405.07972.
  46. A. Bagchi, P. Dhivakar, and S. Dutta, AdS Witten diagrams to Carrollian correlators, J. High Energy Phys. 04 (2023) 135.
  47. H. Kawai, D. C. Lewellen, and S. H. H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B69, 1 (1986).
  48. Z. Bern, J. J. M. Carrasco, and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78, 085011 (2008).
  49. Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, The duality between color and kinematics and its applications, J. Phys. A 57, 333002 (2024).
  50. T. Adamo, J. J. M. Carrasco, M. Carrillo-González, M. Chiodaroli, H. Elvang, H. Johansson, D. O’Connell, R. Roiban, and O. Schlotterer, Snowmass white paper: The double copy and its applications, arXiv:2204.06547.
  51. N. Arkani-Hamed, M. Pate, A. M. Raclariu, and A. Strominger, Celestial amplitudes from UV to IR, J. High Energy Phys. 08 (2021) 062.
  52. S. Stieberger and T. R. Taylor, Symmetries of celestial amplitudes, Phys. Lett. B 793, 141 (2019).
  53. W. Fan, A. Fotopoulos, S. Stieberger, and T. R. Taylor, On Sugawara construction on celestial sphere, J. High Energy Phys. 09 (2020) 139.
  54. E. Casali and A. Puhm, Double copy for celestial amplitudes, Phys. Rev. Lett. 126, 101602 (2021).
  55. E. Casali and A. Sharma, Celestial double copy from the worldsheet, J. High Energy Phys. 05 (2021) 157.
  56. I. Surubaru and B. Zhu, Conformal blocks from celestial graviton amplitudes, J. High Energy Phys. 06 (2025) 174.
  57. T. He and P. Mitra, Asymptotic symmetries and Weinberg’s soft photon theorem in Minkd+2, J. High Energy Phys. 10 (2019) 213.
  58. R. Gonzo and A. Pokraka, Light-ray operators, detectors and gravitational event shapes, J. High Energy Phys. 05 (2021) 015.
  59. G. Barnich, A. Gomberoff, and H. A. Gonzalez, The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86, 024020 (2012).
  60. C. Duval, G. W. Gibbons, P. A. Horvathy, and P. M. Zhang, Carroll versus Newton and Galilei: Two dual non-Einsteinian concepts of time, Classical Quantum Gravity 31, 085016 (2014).
  61. D. Hansen, N. A. Obers, G. Oling, and B. T. Søgaard, Carroll expansion of general relativity, SciPost Phys. 13, 055 (2022).
  62. S. Baiguera, G. Oling, W. Sybesma, and B. T. Søgaard, Conformal Carroll scalars with boosts, SciPost Phys. 14, 086 (2023).
  63. M. Ben-Shahar and H. Johansson, Off-shell color-kinematics duality for Chern-Simons, J. High Energy Phys. 08 (2022) 035.
  64. B. M. Barker, S. N. Gupta, and R. D. Haracz, One-graviton exchange interaction of elementary particles, Phys. Rev. 149, 1027 (1966).
  65. S. R. Huggins and D. J. Toms, One graviton exchange interaction of nonminimally coupled scalar fields, Classical Quantum Gravity 4, 1509 (1987).
  66. E. D’Hoker, D. Z. Freedman, and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B62, 395 (1999).
  67. D. Simmons-Duffin, TASI lectures on conformal field theory in Lorentzian signature (2019), https://www.desy.de/~bargheer/string-journal-club/presentations/2023-05-16_Sebastian-Harris_Simmons-Duffin:_TASI-Lorentzian-CFT.pdf.
  68. H. H. Zhang, K. X. Feng, S. W. Qiu, A. Zhao, and X. S. Li, On analytic formulas of Feynman propagators in position space, Chin. Phys. C 34, 1576 (2010).
  69. E. D’Hoker, D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, Graviton and gauge boson propagators in AdS(d+1), Nucl. Phys. B62, 330 (1999).
  70. S. Komatsu, M. F. Paulos, B. C. Van Rees, and X. Zhao, Landau diagrams in AdS and S-matrices from conformal correlators, J. High Energy Phys. 11 (2020) 046.
  71. A. Bissi, A. Sinha, and X. Zhou, Selected topics in analytic conformal bootstrap: A guided journey, Phys. Rep. 991, 1 (2022).
  72. A. Denner, U. Nierste, and R. Scharf, A compact expression for the scalar one loop four point function, Nucl. Phys. B67, 637 (1991).
  73. N. I. Usyukina and A. I. Davydychev, An approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298, 363 (1993).
  74. J. L. Bourjaily, H. Hannesdottir, A. J. McLeod, M. D. Schwartz, and C. Vergu, Sequential discontinuities of Feynman integrals and the Monodromy Group, J. High Energy Phys. 01 (2021) 205.
  75. J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, Looking for a bulk point, J. High Energy Phys. 01 (2017) 013.
  76. L. Rastelli, K. Roumpedakis, and X. Zhou, AdS3×S3 tree-level correlators: Hidden six-dimensional conformal symmetry, J. High Energy Phys. 10 (2019) 140.
  77. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The gravitational eikonal: From particle, string and brane collisions to black-hole encounters, Phys. Rep. 1083, 1 (2024).
  78. G. ’t Hooft, Graviton dominance in ultrahigh-energy scattering, Phys. Lett. B 198, 61 (1987).
  79. L. Cornalba, M. S. Costa, J. Penedones, and R. Schiappa, Eikonal approximation in AdS/CFT: From shock waves to four-point functions, J. High Energy Phys. 08 (2007) 019.
  80. E. Keski-Vakkuri, Bulk and boundary dynamics in BTZ black holes, Phys. Rev. D 59, 104001 (1999).
  81. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll stories, J. High Energy Phys. 09 (2023) 148.
  82. B. Chen, H. Sun, and Y. Zheng, Quantization of Carrollian conformal scalar theories, Phys. Rev. D 110, 125010 (2024).
  83. J. Cotler, K. Jensen, S. Prohazka, A. Raz, M. Riegler, and J. Salzer, Quantizing Carrollian field theories, J. High Energy Phys. 10 (2024) 049.
  84. P. Kraus and R. M. Myers, Carrollian partition functions and the flat limit of AdS, J. High Energy Phys. 01 (2025) 183.
  85. P. Kraus and R. M. Myers, Carrollian partition function for bulk Yang-Mills theory, arXiv:2503.00916.
  86. J. Figueroa-O’Farrill, A. Pérez, and S. Prohazka, Quantum Carroll/fracton particles, J. High Energy Phys. 10 (2023) 041.
  87. 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.
  88. L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, Carroll structures, null geometry and conformal isometries, Phys. Rev. D 100, 046010 (2019).
  89. J. Cotler, K. Jensen, S. Prohazka, M. Riegler, and J. Salzer, Soft gravitons in three dimensions, J. High Energy Phys. 07 (2025) 002.
  90. G. Poulias and S. Vandoren, On Carroll partition functions and flat space holography, J. High Energy Phys. 06 (2025) 232.
  91. A. Bagchi, M. Gary, and Zodinmawia, Bondi-Metzner-Sachs bootstrap, Phys. Rev. D 96, 025007 (2017).
  92. A. Bagchi, M. Gary, and Zodinmawia, The nuts and bolts of the BMS bootstrap, Classical Quantum Gravity 34, 174002 (2017).
  93. B. Chen, P. X. Hao, R. Liu, and Z. F. Yu, On Galilean conformal bootstrap, J. High Energy Phys. 06 (2021) 112.
  94. B. Chen and R. Liu, The shadow formalism of Galilean CFT2, J. High Energy Phys. 05 (2023) 224.
  95. B. Chen, P. x. Hao, R. Liu, and Z. f. Yu, On Galilean conformal bootstrap. Part II. ξ=0 sector, J. High Energy Phys. 12 (2022) 019.
  96. E. Hijano, P. Kraus, E. Perlmutter, and R. Snively, Witten diagrams revisited: The AdS geometry of conformal blocks, J. High Energy Phys. 01 (2016) 146.
  97. E. Hijano, P. Kraus, E. Perlmutter, and R. Snively, Semiclassical Virasoro blocks from AdS3 gravity, J. High Energy Phys. 12 (2015) 077.
  98. W. Fan, A. Fotopoulos, S. Stieberger, T. R. Taylor, and B. Zhu, Elements of celestial conformal field theory, J. High Energy Phys. 08 (2022) 213.
  99. Z. f. Yu and B. Chen, Free field realization of the BMS Ising model, J. High Energy Phys. 08 (2023) 116.
  100. P. X. Hao, W. Song, Z. Xiao, and X. Xie, BMS-invariant free fermion models, Phys. Rev. D 109, 025002 (2024).

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