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
  • Editors' Suggestion
  • Letter
  • Open Access

Mellin amplitude for n-gluon scattering in anti–de Sitter spacetime

Jinwei Chu* and Savan Kharel†

  • Department of Physics, University of Chicago, Chicago, Illinois 60637, USA

  • *jinweichu@uchicago.edu
  • †skharel@uchicago.edu

Phys. Rev. D 109, L101901 – Published 2 May, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L101901

Abstract

In AdS/CFT, we introduce a robust method for computing n-point gluon Mellin amplitudes, applicable in various spacetime dimensions. Using the Mellin transform and a recursive algorithm, we efficiently calculate tree-level gluon amplitudes. Our approach simplifies the representation of higher-point amplitudes, eliminating the need for complicated integrations. Crucially, the resulting amplitudes closely mirror those in flat space, allowing a straightforward dictionary between the two settings circumventing explicit calculations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  3. G. Mack, D-independent representation of conformal field theories in D dimensions via transformation to auxiliary dual resonance models. scalar amplitudes, arXiv:0907.2407.
  4. J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, J. High Energy Phys. 03 (2011) 025.
  5. A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, A natural language for AdS/CFT correlators, J. High Energy Phys. 11 (2011) 095.
  6. M. F. Paulos, Towards Feynman rules for Mellin amplitudes, J. High Energy Phys. 10 (2011) 074.
  7. A. Bzowski, P. McFadden, and K. Skenderis, Scalar 3-point functions in CFT: Renormalisation, beta functions and anomalies, J. High Energy Phys. 03 (2016) 066.
  8. S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes, J. High Energy Phys. 02 (2019) 040.
  9. H. Isono, T. Noumi, and G. Shiu, Momentum space approach to crossing symmetric CFT correlators, J. High Energy Phys. 07 (2018) 136.
  10. J. A. Farrow, A. E. Lipstein, and P. McFadden, Double copy structure of CFT correlators, J. High Energy Phys. 02 (2019) 130.
  11. S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes. Part II. Gravitons, J. High Energy Phys. 12 (2019) 135.
  12. A. Bzowski, P. McFadden, and K. Skenderis, Conformal n-point functions in momentum space, Phys. Rev. Lett. 124, 131602 (2020).
  13. H. Isono, T. Noumi, and T. Takeuchi, Momentum space conformal three-point functions of conserved currents and a general spinning operator, J. High Energy Phys. 05 (2019) 057.
  14. S. Albayrak, C. Chowdhury, and S. Kharel, Study of momentum space scalar amplitudes in AdS spacetime, Phys. Rev. D 101, 124043 (2020).
  15. A. Bzowski, P. McFadden, and K. Skenderis, Conformal correlators as simplex integrals in momentum space, J. High Energy Phys. 01 (2021) 192.
  16. S. Jain, R. R. John, and V. Malvimat, Constraining momentum space correlators using slightly broken higher spin symmetry, J. High Energy Phys. 04 (2021) 231.
  17. R. Marotta, K. Skenderis, and M. Verma, Momentum space CFT correlators of non-conserved spinning operators, J. High Energy Phys. 03 (2023) 196.
  18. J. Mei, Amplitude bootstrap in (anti) de Sitter space and the four-point graviton from double copy, arXiv:2305.13894.
  19. S. Kharel and G. Siopsis, Tree-level correlators of scalar and vector fields in AdS/CFT, J. High Energy Phys. 11 (2013) 159.
  20. M. S. Costa, V. Gonçalves, and J. a. Penedones, Spinning AdS propagators, J. High Energy Phys. 09 (2014) 064.
  21. C. Sleight and M. Taronna, Spinning Witten diagrams, J. High Energy Phys. 06 (2017) 100.
  22. M. Nishida and K. Tamaoka, Fermions in geodesic Witten diagrams, J. High Energy Phys. 07 (2018) 149.
  23. S. Albayrak, C. Chowdhury, and S. Kharel, New relation for Witten diagrams, J. High Energy Phys. 10 (2019) 274.
  24. V. Gonçalves, R. Pereira, and X. Zhou, 20′ five-point function from AdS5×S5 supergravity, J. High Energy Phys. 10 (2019) 247.
  25. L. F. Alday, V. Gonçalves, and X. Zhou, Supersymmetric five-point gluon amplitudes in AdS space, Phys. Rev. Lett. 128, 161601 (2022).
  26. A. Bissi, A. Sinha, and X. Zhou, Selected topics in analytic conformal bootstrap: A guided journey, Phys. Rep. 991, 1 (2022).
  27. C. Armstrong, H. Gomez, R. Lipinski Jusinskas, A. Lipstein, and J. Mei, New recursion relations for tree-level correlators in anti–de Sitter spacetime, Phys. Rev. D 106, L121701 (2022).
  28. Y.-Z. Li and J. Mei, Bootstrapping Witten diagrams via differential representation in Mellin space, J. High Energy Phys. 07 (2023) 156.
  29. L. F. Alday, V. Gonçalves, M. Nocchi, and X. Zhou, Six-point AdS gluon amplitudes from flat space and factorization, Phys. Rev. Res. 6, L012041 (2024).
  30. S. J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56, 2459 (1986).
  31. E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252, 189 (2004).
  32. N. Arkani-Hamed, F. Cachazo, and J. Kaplan, What is the simplest quantum field theory?, J. High Energy Phys. 09 (2010) 016.
  33. R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94, 181602 (2005).
  34. Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105, 061602 (2010).
  35. J. Chu and S. Kharel, companion article, Toward the Feynman rule for n-point gluon Mellin amplitudes in AdS/CFT, Phys. Rev. D 109, 106003 (2024).
  36. I. Balitsky, Mellin representation of the graviton bulk-to-bulk propagator in AdS, Phys. Rev. D 83, 087901 (2011).
  37. S. Giombi, C. Sleight, and M. Taronna, Spinning AdS loop diagrams: Two point functions, J. High Energy Phys. 06 (2018) 030.
  38. S. Albayrak and S. Kharel, Spinning loop amplitudes in anti–de Sitter space, Phys. Rev. D 103, 026004 (2021).
  39. L. F. Alday, A. Bissi, and X. Zhou, One-loop gluon amplitudes in AdS, J. High Energy Phys. 02 (2022) 105.
  40. N. Arkani-Hamed, D. Baumann, H. Lee, and G. L. Pimentel, The cosmological bootstrap: Inflationary correlators from symmetries and singularities, J. High Energy Phys. 04 (2020) 105.
  41. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, The cosmological bootstrap: Weight-shifting operators and scalar seeds, J. High Energy Phys. 12 (2020) 204.
  42. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, The cosmological bootstrap: Spinning correlators from symmetries and factorization, SciPost Phys. 11, 071 (2021).
  43. C. Sleight and M. Taronna, Bootstrapping inflationary correlators in Mellin space, J. High Energy Phys. 02 (2020) 098.
  44. C. Sleight and M. Taronna, From dS to AdS and back, J. High Energy Phys. 12 (2021) 074.
  45. S. Raju, Four point functions of the stress tensor and conserved currents in AdS4/CFT3, Phys. Rev. D 85, 126008 (2012).
  46. S. Raju, New recursion relations and a flat space limit for AdS/CFT correlators, Phys. Rev. D 85, 126009 (2012).
  47. S. Albayrak and S. Kharel, All plus four point (A)dS graviton function using generalized on-shell recursion relation, J. High Energy Phys. 05 (2023) 151.
  48. S. Albayrak, S. Kharel, and D. Meltzer, On duality of color and kinematics in (A)dS momentum space, J. High Energy Phys. 03 (2021) 249.
  49. C. Armstrong, A. E. Lipstein, and J. Mei, Color/kinematics duality in AdS4, J. High Energy Phys. 02 (2021) 194.
  50. P. Diwakar, A. Herderschee, R. Roiban, and F. Teng, BCJ amplitude relations for anti-de Sitter boundary correlators in embedding space, J. High Energy Phys. 10 (2021) 141.
  51. X. Zhou, Double copy relation in AdS space, Phys. Rev. Lett. 127, 141601 (2021).
  52. S. Jain, R. R. John, A. Mehta, A. A. Nizami, and A. Suresh, Double copy structure of parity-violating CFT correlators, J. High Energy Phys. 07 (2021) 033.
  53. A. Herderschee, R. Roiban, and F. Teng, On the differential representation and color-kinematics duality of AdS boundary correlators, J. High Energy Phys. 05 (2022) 026.
  54. C. Cheung, J. Parra-Martinez, and A. Sivaramakrishnan, On-shell correlators and color-kinematics duality in curved symmetric spacetimes, J. High Energy Phys. 05 (2022) 027.
  55. C. Armstrong, H. Goodhew, A. Lipstein, and J. Mei, Graviton trispectrum from gluons, J. High Energy Phys. 08 (2023) 206.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation