- 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

Holographic one-point functions and geodesics in Schwarzschild dS3

Arundhati Goldar*, Nirmalya Kajuri†, and Rhitaparna Pal‡

  • School of Physical Sciences, IIT Mandi, Himachal Pradesh 175005, India

  • *Contact author: d21086@students.iitmandi.ac.in
  • †Contact author: nirmalya@iitmandi.ac.in
  • ‡Contact author: d21089@students.iitmandi.ac.in
PDF

Phys. Rev. D 114, 066015 – Published 23 September, 2026

DOI: https://doi.org/10.1103/7hqt-b6r2

Abstract

Grinberg and Maldacena showed that heavy thermal one-point functions in AdS/CFT can encode complex geodesics reaching a black hole singularity. We study the de Sitter analog in three-dimensional Schwarzschild–de Sitter space, restricting to the finite cyclic quotients dS3/Zq. We define a one-point function through a differentiate dictionary and show that an analogous result holds for the Bunch-Davies-prepared integral. Using the exact light-field Green’s function, the bulk integral reduces exactly to a convergent one-dimensional transform, whose large-mass limit is controlled by the near-defect region and governed by a complex saddle. Its action reproduces a complex geodesic length from future infinity to the conical defect, whose real part is the renormalized boundary-to-horizon proper time and whose imaginary part is the horizon-to-defect distance. The imaginary part appears in the one-point coefficient normalized in the Lorentzian source basis; in the Euclidean basis the same saddle contributes only the real part, the two being related by a fixed connection factor.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. Juan Martin Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428, 105 (1998).
  3. Edward Witten, Anti de Sitter space, and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  4. Matan Grinberg and Juan Maldacena, Proper time to the black hole singularity from thermal one-point functions, J. High Energy Phys. 03 (2021) 131.
  5. David Berenstein and Robinson Mancilla, Aspects of thermal one-point functions and response functions in AdS black holes, Phys. Rev. D 107, 126010 (2023).
  6. Justin R. David and Srijan Kumar, Thermal one point functions, large d and interior geometry of black holes, J. High Energy Phys. 03 (2023) 256.
  7. Justin R. David and Srijan Kumar, Thermal one-point functions: CFT’s with fermions, large d and large spin, J. High Energy Phys. 10 (2023) 143.
  8. Kaustubh Singhi, Proper time to the singularity and thermal correlators, Phys. Rev. D 112, 106011 (2025).
  9. Justin R. David and Srijan Kumar, One point functions in large N vector models at finite chemical potential, J. High Energy Phys. 01 (2025) 080.
  10. P. Dey, A. Goldar, and N. Kajuri, Geodesics, one-point functions, and black hole perturbations, Phys. Rev. D 114, 026037 (2026).
  11. Andrew Strominger, The dS/CFT correspondence, J. High Energy Phys. 10 (2001) 034.
  12. Edward Witten, Quantum gravity in de Sitter space, arXiv:hep-th/0106109.
  13. Juan Martin Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, J. High Energy Phys. 05 (2003) 013.
  14. Paul McFadden and Kostas Skenderis, Holography for cosmology, Phys. Rev. D 81, 021301 (2010).
  15. Dionysios Anninos, Thomas Hartman, and Andrew Strominger, Higher spin realization of the dS/CFT correspondence, Classical Quantum Gravity 34, 015009 (2017).
  16. D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621.
  17. Per Kraus and Alexander Maloney, A Cardy formula for three-point coefficients or how the black hole got its spots, J. High Energy Phys. 05 (2017) 160.

  18. The quotient used here is the untwisted angular quotient at fixed Lorentzian time. Its Euclidean continuation is correspondingly the singular orbifold with the same fixed conical locus. This should be distinguished from smooth Lens-space quotients of S3, which involve a free action mixing the Euclidean time and angular circles and prepare different static-patch states [19].

  19. Alejandra Castro, Nima Lashkari, and Alexander Maloney, A de Sitter Farey tail, Phys. Rev. D 83, 124027 (2011).
  20. Maximo Banados, Claudio Teitelboim, and Jorge Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69, 1849 (1992).
  21. S Deser and R Jackiw, Three-dimensional cosmological gravity: Dynamics of constant curvature, Ann. Phys. (N.Y.) 153, 405 (1984).
  22. Daniel Z. Freedman, Samir D. Mathur, Alec Matusis, and Leonardo Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence, Nucl. Phys. B546, 96 (1999).
  23. J. B. Hartle and S. W. Hawking, Wave function of the Universe, Phys. Rev. D 28, 2960 (1983).
  24. Dionysios Anninos, Tarek Anous, Daniel Z. Freedman, and George Konstantinidis, Late-time structure of the Bunch-Davies de Sitter wavefunction, J. Cosmol. Astropart. Phys. 11 (2015) 048.
  25. Sebastian Fischetti, Donald Marolf, and Aron C. Wall, A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors, Classical Quantum Gravity 32, 065011 (2015).
  26. Shira Chapman, Damián A. Galante, Eleanor Harris, Sameer U. Sheorey, and David Vegh, Complex geodesics in de Sitter space, J. High Energy Phys. 03 (2023) 006.
  27. Lars Aalsma, Mir Mehedi Faruk, Jan Pieter van der Schaar, Manus R. Visser, and Job de Witte, Late-time correlators and complex geodesics in de Sitter space, SciPost Phys. 15, 031 (2023).
  28. T. S. Bunch and P. C. W. Davies, Quantum field theory in de Sitter space: Renormalization by point splitting, Proc. R. Soc. A 360, 117 (1978).
  29. Dionysios Anninos, Gim Seng Ng, and Andrew Strominger, Future boundary conditions in de Sitter space, J. High Energy Phys. 02 (2012) 032.
  30. 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 1.2.7 of 2026-06-15).

Outline

Information

Phys. Rev. D 114, 066015– Published 23 September, 2026
  • Received 1 April 2026
  • Accepted 31 August 2026
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