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Proper time to the singularity and thermal correlators

Kaustubh Singhi*

  • *Contact author: kaustubh.singhi@icts.res.in
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Phys. Rev. D 112, 106011 – Published 17 November, 2025

DOI: https://doi.org/10.1103/n2n1-1d9f

Abstract

We study certain higher-point thermal correlators of heavy and light scalar primaries in a holographic conformal field theory. Assuming simple self-interactions and couplings of the scalars in the bulk theory, we show that the thermal correlators contain a signature of the proper time to singularity from the horizon. The key idea is to use Wentzel-Kramers-Brillouin approximations for the propagators and evaluate the bulk integrals using saddle point method.

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References (27)

  1. P. Kraus, H. Ooguri, and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67, 124022 (2003).
  2. L. Fidkowski, V. Hubeny, M. Kleban, and S. Shenker, The black hole singularity in AdS/CFT, J. High Energy Phys. 02 (2004) 014.
  3. G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., J. High Energy Phys. 04 (2005) 044.
  4. G. T. Horowitz, H. Leung, L. Queimada, and Y. Zhao, Boundary signature of singularity in the presence of a shock wave, SciPost Phys. 16, 060 (2024).
  5. N. Čeplak, H. Liu, A. Parnachev, and S. Valach, Black hole singularity from OPE, J. High Energy Phys. 10 (2024) 105.
  6. M. Grinberg and J. Maldacena, Proper time to the black hole singularity from thermal one-point functions, J. High Energy Phys. 03 (2020) 131.
  7. J. Louko, D. Marolf, and S. F. Ross, Geodesic propagators and black hole holography, Phys. Rev. D 62, 044041 (2000).
  8. J. R. David and S. Kumar, Thermal one point functions, large d and interior geometry of black holes, J. High Energy Phys. 03 (2023) 256.
  9. J. R. David and S. Kumar, Thermal one-point functions: CFT’s with fermions, large d and large spin, J. High Energy Phys. 10 (2023) 143.
  10. D. Rodriguez-Gomez and J. G. Russo, Correlation functions in finite temperature CFT and black hole singularities, J. High Energy Phys. 06 (2021) 048.
  11. D. Rodriguez-Gomez and J. G. Russo, Thermal correlation functions in CFT and factorization, J. High Energy Phys. 11 (2021) 049.
  12. H. Krishna and D. Rodriguez-Gomez, Holographic thermal correlators revisited, J. High Energy Phys. 11 (2021) 139.
  13. G. Georgiou and D. Zoakos, Holographic correlation functions at finite density and/or finite temperature, J. High Energy Phys. 11 (2022) 087.
  14. G. Georgiou and D. Zoakos, Holographic three-point correlators at finite density and temperature, J. High Energy Phys. 12 (2023) 125.
  15. D. Z. Freedman and A. Van Proeyen, The AdS/CFT correspondence, in Supergravity (Cambridge University Press, Cambridge, England, 2012), pp. 527–572.
  16. I. Amado and C. Hoyos-Badajoz, AdS black holes as reflecting cavities, J. High Energy Phys. 09 (2008) 118.
  17. T. Kawai and Y. Takei, Algebraic Analysis of Singular Perturbation Theory, Iwanami Series in Modern Mathematics (American Mathematical Society, Providence, 2005).
  18. D. Birmingham, Topological black holes in anti-de Sitter space, Classical Quantum Gravity 16, 1197 (1999).
  19. R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. (N.Y.) 35, 4217 (1994).
  20. C. Jana, R. Loganayagam, and M. Rangamani, Open quantum systems and Schwinger-Keldysh holograms, J. High Energy Phys. 07 (2020) 242.
  21. I. S. Gradshteyn and I. M. Ryszhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier/Academic Press, Amsterdam, 2007), Translated from the Russian, Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, With one CD-ROM (Windows, Macintosh and UNIX).
  22. M. Cvitković, A.-S. Smith, and J. Pande, Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps, J. Phys. A 50, 265206 (2017).
  23. R. B. Paris, Asymptotics of the Gauss hypergeometric function with large parameters, I, J. Class. Anal. 2, 183 (2013).
  24. DLMF, NIST Digital Library of Mathematical Functions, edited by F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, https://dlmf.nist.gov/, (Release 1.2.4 of 2025-03-15).
  25. R. B. Paris, Asymptotics of the Gauss hypergeometric function with large parameters, II, J. Class. Anal. 3, 1 (2013).
  26. D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence, Nucl. Phys. B546, 96 (1999).
  27. D. Berenstein and R. Mancilla, Aspects of thermal one-point functions and response functions in AdS black holes, Phys. Rev. D 107, 126010 (2023).

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Phys. Rev. D 112, 106011– Published 17 November, 2025
  • Received 19 May 2025
  • Accepted 28 October 2025
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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.

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