- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Celestial closed strings at one loop

Anthonny F. Canazas Garay1, Gaston Giribet2, Yoel Parra-Cisterna3, and Francisco Rojas4

PDF

Phys. Rev. D 111, 126014 – Published 18 June, 2025

DOI: https://doi.org/10.1103/3jqt-k1sl

Abstract

In this paper we continue our investigation of superstring scattering amplitudes in the conformal basis. We focus on the case of the four-graviton scattering processes at one loop in closed superstring theory. We write the expression for such a process in the celestial variables and confirm previous expectations. In particular, we find the adequate overall factorization of the α′ dependence which organizes the loop expansion of closed string celestial amplitudes. We also show that, at one loop, the field theory limit, when properly defined, commutes with the Mellin transform of the amplitudes for all values of the conformally invariant cross-ratio, something that had already been observed for gluon processes at one loop in open string theory and is to be compared with the tree-level computations. This indicates that many of the features satisfied for open string gluon amplitudes at tree and one-loop levels are also universal properties of graviton celestial amplitudes in closed string theory. As a by-product, we also compute field theory graviton amplitudes at one loop in the conformal basis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (28)

  1. S. Pasterski, S. H. Shao, and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96, 065026 (2017).
  2. S. Pasterski and S. H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017).
  3. S. Pasterski, S. H. Shao, and A. Strominger, Gluon amplitudes as 2d conformal correlators, Phys. Rev. D 96, 085006 (2017).
  4. S. Stieberger and T. R. Taylor, Strings on celestial sphere, Nucl. Phys. B935, 388 (2018).
  5. S. Stieberger and T. R. Taylor, Superstring/supergravity Mellin correspondence in Grassmannian formulation, Phys. Lett. B 725, 180 (2013).
  6. S. Stieberger and T. R. Taylor, Superstring amplitudes as a Mellin transform of supergravity, Nucl. Phys. B873, 65 (2013).
  7. L. Castiblanco, G. Giribet, G. Marin, and F. Rojas, Celestial strings: Field theory, conformally soft limits, and mapping the worldsheet onto the celestial sphere, Phys. Rev. D 110, 126001 (2024).
  8. L. Donnay, G. Giribet, H. González, A. Puhm, and F. Rojas, Celestial open strings at one-loop, J. High Energy Phys. 10 (2023) 047.
  9. D. Bockisch, Celestial string integrands & their expansions, Nucl. Phys. B1011, 116792 (2025).
  10. J. Polchinski, String Theory. Vol. 1: An Introduction to the Bosonic String (Cambridge University Press, Cambridge, England, 2007).
  11. G. ’t Hooft and M. J. G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincare A Phys. Theor. 20, 69 (1974).
  12. S. Sannan, Gravity as the limit of the type II superstring theory, Phys. Rev. D 34, 1749 (1986).
  13. D. C. Dunbar and P. S. Norridge, Calculation of graviton scattering amplitudes using string based methods, Nucl. Phys. B433, 181 (1995).
  14. J. F. Donoghue and T. Torma, Infrared behavior of graviton-graviton scattering, Phys. Rev. D 60, 024003 (1999).
  15. M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory Vol. 2: 25th Anniversary Edition (Cambridge University Press, Cambridge, England, 2012).
  16. M. B. Green, J. H. Schwarz, and L. Brink, N=4 Yang-Mills and N=8 supergravity as limits of string theories, Nucl. Phys. B198, 474 (1982).
  17. J. H. Schwarz, Superstring theory, Phys. Rep. 89, 223 (1982).
  18. A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448.
  19. S. Pasterski, M. Pate, and A. M. Raclariu, Celestial holography, arXiv:2111.11392.
  20. L. Donnay, S. Pasterski, and A. Puhm, Asymptotic symmetries and celestial CFT, J. High Energy Phys. 09 (2020) 176.
  21. N. Arkani-Hamed, M. Pate, A. M. Raclariu, and A. Strominger, Celestial amplitudes from UV to IR, J. High Energy Phys. 08 (2021) 062.
  22. M. Pate, A. M. Raclariu, A. Strominger, and E. Y. Yuan, Celestial operator products of gluons and gravitons, Rev. Math. Phys. 33, 2140003 (2021).
  23. E. Himwich, S. A. Narayanan, M. Pate, N. Paul, and A. Strominger, The soft S-matrix in gravity, J. High Energy Phys. 09 (2020) 129.
  24. H. A. González, A. Puhm, and F. Rojas, Loop corrections to celestial amplitudes, Phys. Rev. D 102, 126027 (2020).
  25. S. Stieberger, T. R. Taylor, and B. Zhu, Carrollian amplitudes from strings, J. High Energy Phys. 04 (2024) 127.
  26. A. Puhm, Conformally soft theorem in gravity, J. High Energy Phys. 09 (2020) 130.
  27. M. Borji and Y. Pano, Distributional celestial amplitudes, J. High Energy Phys. 07 (2024) 120.
  28. X. Kervyn and S. Stieberger, High energy string theory and the celestial sphere, arXiv:2504.13738.

Outline

Information

Phys. Rev. D 111, 126014– Published 18 June, 2025
  • Received 1 May 2025
  • Accepted 5 June 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation