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Thermal spectral function asymptotics and black hole singularity in holography

Hewei Frederic Jia1,* and Mukund Rangamani2,†

  • 1Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
  • 2Center for Quantum Mathematics and Physics (QMAP), Department of Physics and Astronomy, University of California, Davis, California 95616, USA

  • *Contact author: heweifred@gmail.com
  • †Contact author: mukund@physics.ucdavis.edu
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Phys. Rev. D 114, 046025 – Published 25 August, 2026

DOI: https://doi.org/10.1103/tzm2-jjvg

Abstract

We investigate the analytic structure of thermal spectral function of holographic conformal field theories (CFTs), synthesizing recent developments into a set of observations about its asymptotics. Specifically, for a class of scalar primaries with integral dimension, we demonstrate factorization of the exact spectral function into a polynomial piece, which captures the vacuum dynamics, and a nonperturbative piece, which controls its asymptotics. Using exact WKB techniques, we derive a transseries expression for the latter. We use this information to deduce the singular loci of a spatially averaged thermofield double correlator in the complex time plane. Such singularities have been argued to encode information regarding the black hole singularity in the dual spacetime. Our results give a refinement of these statements by capturing the momentum dependence.

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References (34)

  1. L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter, and D. Simmons-Duffin, The conformal bootstrap at finite temperature, J. High Energy Phys. 10 (2018) 070.
  2. G. Aminov, A. Grassi, and Y. Hatsuda, Black hole quasinormal modes and Seiberg–Witten theory, Ann. Henri Poincare 23, 1951 (2022).
  3. G. Bonelli, C. Iossa, D. Panea Lichtig, and A. Tanzini, Irregular Liouville correlators and connection formulae for Heun functions, Commun. Math. Phys. 397, 635 (2023).
  4. O. Lisovyy and A. Naidiuk, Perturbative connection formulas for Heun equations, J. Phys. A 55, 434005 (2022).
  5. M. Dodelson, A. Grassi, C. Iossa, D. Panea Lichtig, and A. Zhiboedov, Holographic thermal correlators from supersymmetric instantons, arXiv:2206.07720.
  6. K. Iwaki and T. Nakanishi, Exact WKB analysis and cluster algebras, J. Phys. A 47, 474009 (2014).
  7. K. Iwaki and T. Nakanishi, Exact wkb analysis and cluster algebras II: Simple poles, orbifold points, and generalized cluster algebras, Int. Math. Res. Not. 2016, 4375 (2015).
  8. L. Fidkowski, V. Hubeny, M. Kleban, and S. Shenker, The black hole singularity in AdS/CFT, J. High Energy Phys. 02 (2003) 014.
  9. J. Louko, D. Marolf, and S. F. Ross, On geodesic propagators and black hole holography, Phys. Rev. D 62, 044041 (2000).
  10. P. Kraus, H. Ooguri, and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67, 124022 (2003).
  11. G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., J. High Energy Phys. 04 (2005) 044.
  12. I. Amado and C. Hoyos-Badajoz, AdS black holes as reflecting cavities, J. High Energy Phys. 09 (2008) 118.
  13. G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett. 2, 221 (2009).
  14. N. Čeplak, H. Liu, A. Parnachev, and S. Valach, Black hole singularity from OPE, J. High Energy Phys. 10 (2024) 105.
  15. N. Afkhami-Jeddi, S. Caron-Huot, J. Chakravarty, and A. Maloney, Imprint of the black hole singularity on thermal two-point functions, arXiv:2510.21673.
  16. N. Čeplak, H. Liu, A. Parnachev, and S. Valach, Fooling the censor: Going beyond inner horizons with the OPE, arXiv:2511.09638.
  17. M. Dodelson, Ringdown in the SYK model, SciPost Phys. 19, 081 (2025).
  18. M. Dodelson, C. Iossa, and R. Karlsson, Bouncing off a stringy singularity, arXiv:2511.09616.
  19. H. F. Jia and M. Rangamani, Exact holographic thermal spectral functions: OPE, non-perturbative corrections, and black hole singularity, arXiv:2604.10803.
  20. A. Manenti, Thermal CFTs in momentum space, J. High Energy Phys. 01 (2019) 009.
  21. L. F. Alday, M. Kologlu, and A. Zhiboedov, Holographic correlators at finite temperature, J. High Energy Phys. 06 (2020) 082.
  22. I. Burić, I. Gusev, and A. Parnachev, Thermal holographic correlators and KMS condition, J. High Energy Phys. 09 (2025) 053.
  23. J. Barrat, D. N. Bozkurt, E. Marchetto, A. Miscioscia, and E. Pomoni, The analytic bootstrap at finite temperature, arXiv:2506.06422.
  24. I. Burić, I. Gusev, and A. Parnachev, Holographic correlators from thermal bootstrap, arXiv:2508.08373.
  25. J. Barrat, D. N. Bozkurt, E. Marchetto, A. Miscioscia, and E. Pomoni, Analytic thermal bootstrap meets holography, arXiv:2510.20894.
  26. S. Caron-Huot, Asymptotics of thermal spectral functions, Phys. Rev. D 79, 125009 (2009).
  27. M. Dodelson, C. Iossa, R. Karlsson, and A. Zhiboedov, A thermal product formula, J. High Energy Phys. 01 (2023) 036.
  28. H. F. Jia and M. Rangamani, Holographic thermal correlators and quasinormal modes from semiclassical virasoro blocks, J. High Energy Phys. 12 (2024) 047.
  29. R. C. Myers, A. O. Starinets, and R. M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, J. High Energy Phys. 11 (2007) 091.
  30. D. T. Son and A. O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, J. High Energy Phys. 09 (2002) 042.
  31. T. Kawai and Y. Takei, Algebraic Analysis of Singular Perturbation Theory, Translations of Mathematical Monographs Vol. 227 (American Mathematical Society, Providence, RI, 2005), p. 129, Iwanami Series in Modern Mathematics.
  32. E. Delabaere, H. Dillinger, and F. Pham, Exact semiclassical expansions for one-dimensional quantum oscillators, J. Math. Phys. (N.Y.) 38, 6126 (1997).
  33. A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. l’IHP Phys. Théor. 39, 211 (1983).
  34. D. Teaney, Finite temperature spectral densities of momentum and R-charge correlators in N=4 Yang Mills theory, Phys. Rev. D 74, 045025 (2006).

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Phys. Rev. D 114, 046025– Published 25 August, 2026
  • Received 2 February 2026
  • Accepted 15 July 2026
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