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Ramp and plateau in bulk correlators within the disk topology in Jackiw-Teitelboim gravity

Cristiano Germani* and Mickael Komendyak

  • Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain

  • *Contact author: germani@icc.ub.edu
  • Contact author: komendyak@icc.ub.edu

Phys. Rev. D 113, 126016 – Published 10 June, 2026

DOI: https://doi.org/10.1103/37dn-cdf1

Abstract

We study bulk two-point correlation functions of a massless scalar field in Jackiw-Teitelboim gravity around the eternal black hole saddle. While same-side correlators exhibit exponential decay, two-sided correlators, at the next-to-leading order in steepest-descent approximation, exhibit a ramp followed by a plateau after the initial semiclassical exponential decay. Our results indicate that the late-time saturation of two-sided correlators is already visible within the perturbative saddle expansion of the bulk path integral, without invoking nonperturbative eS effects. Finally, we show that the dip time, defined as the minimum of the correlator, grows inversely with the black hole temperature, consistent with expectations from the holographic dual.

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References (33)

  1. S. W. Hawking, Nature (London) 248, 30 (1974).
  2. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  3. S. W. Hawking, Phys. Rev. D 14, 2460 (1976).
  4. D. N. Page, Phys. Rev. Lett. 71, 3743 (1993).
  5. D. N. Page, Phys. Rev. Lett. 71, 1291 (1993).
  6. R. Jackiw, Nucl. Phys. B252, 343 (1985).
  7. C. Teitelboim, Phys. Lett. 126B, 41 (1983).
  8. J. Maldacena, D. Stanford, and Z. Yang, Prog. Theor. Exp. Phys. (2016) 12C104.
  9. A. Almheiri and J. Polchinski, J. High Energy Phys. 11 (2015) 014.
  10. J. Engelsöy, T. G. Mertens, and H. Verlinde, J. High Energy Phys. 07 (2016) 139.
  11. S. Sachdev, Phys. Rev. Lett. 105, 151602 (2010).
  12. J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, J. High Energy Phys. 05 (2017) 118; 09 (2018) 2.
  13. J. Maldacena and D. Stanford, Phys. Rev. D 94, 106002 (2016).
  14. P. Saad, S. H. Shenker, and D. Stanford, arXiv:1806.06840.
  15. P. Saad, S. H. Shenker, and D. Stanford, arXiv:1903.11115.
  16. P. Saad, arXiv:1910.10311.
  17. D. Stanford and E. Witten, Adv. Theor. Math. Phys. 24, 1475 (2020).
  18. T. G. Mertens and G. J. Turiaci, Living Rev. Relativity 26, 4 (2023).
  19. A. Blommaert, T. G. Mertens, and H. Verschelde, J. High Energy Phys. 09 (2019) 060.
  20. D. Marolf and H. Maxfield, J. High Energy Phys. 08 (2020) 044.
  21. P. Saad, S. H. Shenker, D. Stanford, and S. Yao, J. High Energy Phys. 09 (2024) 133.
  22. C. Germani, Phys. Rev. D 106, 066018 (2022).
  23. M. Spradlin and A. Strominger, J. High Energy Phys. 11 (1999) 021.
  24. U. H. Danielsson, E. Keski-Vakkuri, and M. Kruczenski, J. High Energy Phys. 01 (1999) 002.
  25. W. G. Unruh, Phys. Rev. D 14, 870 (1976).
  26. J. M. Maldacena, J. High Energy Phys. 04 (2003) 021.
  27. J. Maldacena and L. Susskind, Fortschr. Phys. 61, 781 (2013).
  28. S. Ryu and T. Takayanagi, J. High Energy Phys. 08 (2006) 045.
  29. D. Stanford and E. Witten, J. High Energy Phys. 10 (2017) 008.
  30. Y.-H. Qi, Y. Seo, S.-J. Sin, and G. Song, Phys. Rev. D 99, 066001 (2019).
  31. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  32. T. G. Mertens, G. J. Turiaci, and H. L. Verlinde, J. High Energy Phys. 08 (2017) 136.
  33. L. Griguolo, J. Papalini, and D. Seminara, J. High Energy Phys. 05 (2021) 140.

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