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  • Open Access

Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space

Bo Wang (王波)*, Di Wu (吴迪)†, and Ellis Ye Yuan (袁野)‡

  • Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou, Zhejiang 310058, China and Joint Center for Quanta-to-Cosmos Physics, Zhejiang University, Hangzhou, Zhejiang 310058, China

  • *Contact author: b_w@zju.edu.cn
  • †Contact author: stevediwu@zju.edu.cn
  • ‡Contact author: eyyuan@zju.edu.cn
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Phys. Rev. Lett. 135, 041603 – Published 24 July, 2025

DOI: https://doi.org/10.1103/v72s-rv7y

Abstract

We bootstrap the first-order correction in the curvature expansion of the Virasoro-Shapiro amplitude in AdS spacetime, for arbitrary Kaluza-Klein charges of external operators. By constructing a universal ansatz based on single-valued multiple polylogarithms as well as an AdS×S formalism, and matching it with the low-lying result, we derive a unified formula in terms of world-sheet integrals. Our result predicts an infinite number of Wilson coefficients that were not available in previous literature.

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References (49)

  1. S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS5×S5 supergravity: Hidden ten-dimensional conformal symmetry, J. High Energy Phys. 01 (2019) 196.

  2. For recent explorations, see Refs. [3, 4, 5, 6, 7].

  3. F. Aprile and P. Vieira, Large p explorations. from SUGRA to big STRINGS in Mellin space, J. High Energy Phys. 12 (2020) 206.
  4. J. M. Drummond, D. Nandan, H. Paul, and K. S. Rigatos, String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM, J. High Energy Phys. 12 (2019) 173.
  5. J. M. Drummond, H. Paul, and M. Santagata, Bootstrapping string theory on AdS5×S5, Phys. Rev. D 108, 026020 (2023).
  6. T. Abl, P. Heslop, and A. E. Lipstein, Towards the Virasoro-Shapiro amplitude in AdS5×S5, J. High Energy Phys. 04 (2021) 237.
  7. F. Aprile, J. M. Drummond, H. Paul, and M. Santagata, The Virasoro-Shapiro amplitude in AdS5×S5 and level splitting of 10d conformal symmetry, J. High Energy Phys. 11 (2021) 109.
  8. L. F. Alday, T. Hansen, and J. A. Silva, Emergent worldsheet for the AdS Virasoro-Shapiro amplitude, Phys. Rev. Lett. 131, 161603 (2023).
  9. L. F. Alday and T. Hansen, The AdS Virasoro-Shapiro amplitude, J. High Energy Phys. 10 (2023) 023.
  10. G. Fardelli, T. Hansen, and J. A. Silva, AdS Virasoro-Shapiro amplitude with KK modes, J. High Energy Phys. 11 (2023) 064.
  11. L. F. Alday, T. Hansen, and J. A. Silva, AdS Virasoro-Shapiro from dispersive sum rules, J. High Energy Phys. 10 (2022) 036.
  12. L. F. Alday, T. Hansen, and J. A. Silva, AdS Virasoro-Shapiro from single-valued periods, J. High Energy Phys. 12 (2022) 010.
  13. D. J. Binder, S. M. Chester, S. S. Pufu, and Y. Wang, N=4 Super-Yang-Mills correlators at strong coupling from string theory and localization, J. High Energy Phys. 12 (2019) 119.
  14. A. Brown, P. Heslop, C. Wen, and H. Xie, Integrated correlators in N=4 SYM beyond localisation, Phys. Rev. Lett. 132, 101602 (2024).
  15. B. Eden, A. C. Petkou, C. Schubert, and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N=4 SYM and AdS/CFT, Nucl. Phys. B607, 191 (2001).
  16. M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B711, 409 (2005).

  17. The space-time cross ratios are defined as u=x122x342x132x242,v=x142x232x132x242,xij2=(xi−xj)2.

  18. P. Heslop, The SAGEX review on scattering amplitudes, chapter 8: Half BPS correlators, J. Phys. A 55, 443009 (2022).
  19. L. Rastelli and X. Zhou, Mellin amplitudes for AdS5×S5, Phys. Rev. Lett. 118, 091602 (2017).
  20. L. F. Alday, T. Hansen, and J. A. Silva, On the spectrum and structure constants of short operators in N=4 SYM at strong coupling, J. High Energy Phys. 08 (2023) 214.
  21. O. Schlotterer and O. Schnetz, Closed strings as single-valued open strings: A genus-zero derivation, J. Phys. A 52, 045401 (2019).
  22. F. Brown and C. Dupont, Single-valued integration and double copy, J. Reine Angew. Math. 2021, 145 (2021).
  23. P. Vanhove and F. Zerbini, Single-valued hyperlogarithms, correlation functions and closed string amplitudes, Adv. Theor. Math. Phys. 26, 455 (2022).
  24. F. Brown and C. Dupont, Single-valued integration and superstring amplitudes in genus zero, Commun. Math. Phys. 382, 815 (2021).
  25. Z. Huang, B. Wang, E. Y. Yuan, and J. Zhang, All five-point Kaluza-Klein correlators and hidden 8d symmetry in AdS5×S3, Phys. Rev. Lett. 134, 161601 (2025).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/v72s-rv7y for the explicit expressions of the function basis and a brief review on SVMPLs. Multiple polylogarithms (MPLs) are defined through iterated integrals [27,28], and SVMPLs are constructed following [29]. This can be conveniently implemented using PolyLogTools [30].
  27. A. B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5, 497 (1998).
  28. A. B. Goncharov, Multiple polylogarithms and mixed Tate motives, arXiv:math/0103059.
  29. F. C. S. Brown, Polylogarithmes multiples uniformes en une variable, C. R. Math. 338, 527 (2004).
  30. C. Duhr and F. Dulat, PolyLogTools—polylogs for the masses, J. High Energy Phys. 08 (2019) 135.
  31. N. Gromov, A. Hegedus, J. Julius, and N. Sokolova, Fast QSC solver: Tool for systematic study of N=4 Super-Yang-Mills spectrum, J. High Energy Phys. 05 (2024) 185.
  32. J. Julius and N. Sokolova, Conformal field theory-data analysis for N=4 Super-Yang-Mills at strong coupling, J. High Energy Phys. 03 (2024) 090.
  33. J. Julius and N. S. Sokolova, Unmixing sub-leading Regge trajectories of N=4 Super-Yang-Mills, J. High Energy Phys. 04 (2025) 200.
  34. L. F. Alday, T. Hansen, and M. Nocchi, High energy string scattering in AdS, J. High Energy Phys. 02 (2024) 089.
  35. L. F. Alday, M. Nocchi, C. Virally, and X. Zhou, On the Regge behaviour of the AdS Virasoro-Shapiro Amplitude, J. High Energy Phys. 04 (2025) 064.
  36. X. Fa, B. Wang, D. Wu, and E. Y. Yuan (to be published).
  37. L. F. Alday, G. Giribet, and T. Hansen, On the AdS3 Virasoro-Shapiro amplitude, J. High Energy Phys. 03 (2025) 002.
  38. S. M. Chester and D.-l. Zhong, The AdS3×S3 Virasoro-Shapiro amplitude with RR flux, Phys. Rev. Lett. 134, 151602 (2025).
  39. S. M. Chester, T. Hansen, and D.-l. Zhong, The type IIA Virasoro-Shapiro amplitude in AdS4×CP3 from ABJM theory, J. High Energy Phys. 05 (2025) 040.
  40. L. F. Alday, S. M. Chester, T. Hansen, and D.-l. Zhong, The AdS Veneziano amplitude at small curvature, J. High Energy Phys. 05 (2024) 322.
  41. L. F. Alday and T. Hansen, Single-valuedness of the AdS Veneziano amplitude, J. High Energy Phys. 08 (2024) 108.
  42. L. F. Alday and A. Bissi, Loop corrections to supergravity on AdS5×S5, Phys. Rev. Lett. 119, 171601 (2017).
  43. F. Aprile, J. M. Drummond, P. Heslop, and H. Paul, Quantum gravity from conformal field theory, J. High Energy Phys. 01 (2018) 035.
  44. F. Aprile, J. M. Drummond, P. Heslop, and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, J. High Energy Phys. 05 (2018) 056.
  45. L. F. Alday, On genus-one string amplitudes on AdS5×S5, J. High Energy Phys. 04 (2021) 005.
  46. F. Aprile, J. Drummond, P. Heslop, and H. Paul, One-loop amplitudes in AdS5×S5 supergravity from N=4 SYM at strong coupling, J. High Energy Phys. 03 (2020) 190.
  47. L. F. Alday and X. Zhou, Simplicity of AdS supergravity at one loop, J. High Energy Phys. 09 (2020) 008.
  48. L. F. Alday, S. M. Chester, and T. Hansen, Modular invariant holographic correlators for N=4 SYM with general gauge group, J. High Energy Phys. 12 (2021) 159.
  49. Z. Huang, B. Wang, and E. Y. Yuan, All next-to-next-to-extremal one-loop correlators of AdS supergluons and supergravitons, Phys. Rev. Lett. 134, 051601 (2025).

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Phys. Rev. Lett. 135, 041603– Published 24 July, 2025
  • Received 17 March 2025
  • Revised 1 June 2025
  • Accepted 2 July 2025
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