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  • Letter
  • Open Access

Complex saddles of three-dimensional de Sitter gravity via holography

Heng-Yu Chen1, Yasuaki Hikida2, Yusuke Taki2, and Takahiro Uetoko3

  • 1Department of Physics, National Taiwan University, Taipei 10617, Taiwan
  • 2Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 3Science in General Education, National Institute of Technology, Kushiro College, Hokkaido 084-0916, Japan

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Phys. Rev. D 107, L101902 – Published 24 May, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L101902

Abstract

We determine complex saddles of three-dimensional gravity with a positive cosmological constant by applying the recently proposed holography. It is sometimes useful to consider a complexified metric to study quantum gravity as in the case of the no-boundary proposal by Hartle and Hawking. However, there would be too many saddles for complexified gravity, and we should determine which saddles to take. We describe the gravity theory by three-dimensional SL(2,C) Chern-Simons theory. At the leading order in the Newton constant, its holographic dual is given by Liouville theory with a large imaginary central charge. We examine geometry with a conical defect, called a de Sitter black hole, from a Liouville two-point function. We also consider geometry with two conical defects, whose saddles are determined by the monodromy matrix of Liouville four-point function. Utilizing Chern-Simons description, we extend the similar analysis to the case with higher-spin gravity.

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References (52)

  1. Edward Witten, A note on complex spacetime metrics, arXiv:2111.06514.
  2. J. B. Hartle and S. W. Hawking, Wave function of the universe, Phys. Rev. D 28, 2960 (1983).
  3. Jorma Louko and Rafael D. Sorkin, Complex actions in two-dimensional topology change, Classical Quantum Gravity 14, 179 (1997).
  4. Maxim Kontsevich and Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, J. Q. Math. 72, 673 (2021).
  5. Edward Witten, (2+1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B311, 46 (1988).
  6. Edward Witten, Quantization of Chern-Simons gauge theory with complex gauge group, Commun. Math. Phys. 137, 29 (1991).
  7. Edward Witten, Analytic continuation of Chern-Simons theory, AMS/IP Stud. Adv. Math. 50, 347 (2011).
  8. Yasuaki Hikida, Tatsuma Nishioka, Tadashi Takayanagi, and Yusuke Taki, Holography in de Sitter Space via Chern-Simons Gauge Theory, Phys. Rev. Lett. 129, 041601 (2022).
  9. Yasuaki Hikida, Tatsuma Nishioka, Tadashi Takayanagi, and Yusuke Taki, CFT duals of three-dimensional de Sitter gravity, J. High Energy Phys. 05 (2022) 129.
  10. Heng-Yu Chen and Yasuaki Hikida, Three-Dimensional de Sitter Holography and Bulk Correlators at Late Time, Phys. Rev. Lett. 129, 061601 (2022).
  11. Heng-Yu Chen, Shi Chen, and Yasuaki Hikida, Late-time correlation functions in dS3/CFT2 correspondence, J. High Energy Phys. 02 (2023) 038.
  12. Ivano Basile, Andrea Campoleoni, and Joris Raeymaekers, A note on the admissibility of complex BTZ metrics, J. High Energy Phys. 03 (2023) 187.
  13. Juan Martin Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, J. High Energy Phys. 05 (2003) 013.
  14. Andrew Strominger, The dS/CFT correspondence, J. High Energy Phys. 10 (2001) 034.
  15. Edward Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference (American Mathematical Society, Rhode Island, USA, 2001), arXiv:hep-th/0106109.
  16. Jacob D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973).
  17. G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15, 2752 (1977).
  18. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  19. S. Deser and R. Jackiw, Three-dimensional cosmological gravity: Dynamics of constant curvature, Ann. Phys. (N.Y.) 153, 405 (1984).
  20. Daniel Harlow, Jonathan Maltz, and Edward Witten, Analytic continuation of Liouville theory, J. High Energy Phys. 12 (2011) 071.
  21. Edward Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121, 351 (1989).
  22. Marcus Spradlin, Andrew Strominger, and Anastasia Volovich, Les Houches lectures on de Sitter space, in Les Houches Summer School: Session 76: Euro Summer School on Unity of Fundamental Physics: Gravity, Gauge Theory and Strings (Springer Berlin, Heidelberg, Germany, 2001), pp. 423–453, arXiv:hep-th/0110007.
  23. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  24. Michael Gutperle and Per Kraus, Higher spin black holes, J. High Energy Phys. 05 (2011) 022.
  25. Martin Ammon, Michael Gutperle, Per Kraus, and Eric Perlmutter, Black holes in three dimensional higher spin gravity: A review, J. Phys. A 46, 214001 (2013).
  26. Alexander B. Zamolodchikov and Alexei B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B477, 577 (1996).
  27. Heng-Yu Chen, Yasuaki Hikida, Yusuke Taki, and Takahiro Uetoko (to be published).
  28. Matthias R. Gaberdiel and Rajesh Gopakumar, An AdS3 dual for minimal model CFTs, Phys. Rev. D 83, 066007 (2011).
  29. Thomas Creutzig and Yasuaki Hikida, Correlator correspondences for Gaiotto-Rapčák dualities and first order formulation of coset models, J. High Energy Phys. 12 (2021) 144.
  30. Alejandra Castro, Rajesh Gopakumar, Michael Gutperle, and Joris Raeymaekers, Conical defects in higher spin theories, J. High Energy Phys. 02 (2012) 096.
  31. Matthias R. Gaberdiel and Rajesh Gopakumar, Triality in minimal model holography, J. High Energy Phys. 07 (2012) 127.
  32. Eric Perlmutter, Tomas Prochazka, and Joris Raeymaekers, The semiclassical limit of WN CFTs and Vasiliev theory, J. High Energy Phys. 05 (2013) 007.
  33. Daniel A. Roberts and Douglas Stanford, Two-Dimensional Conformal Field Theory and the Butterfly Effect, Phys. Rev. Lett. 115, 131603 (2015).
  34. Thomas Hartman, Entanglement entropy at large central charge, arXiv:1303.6955.
  35. Gregory W. Moore and Nathan Seiberg, Polynomial equations for rational conformal field theories, Phys. Lett. B 212, 451 (1988).
  36. Gregory W. Moore and Nathan Seiberg, Naturality in conformal field theory, Nucl. Phys. B313, 16 (1989).
  37. Pawel Caputa, Tokiro Numasawa, and Alvaro Veliz-Osorio, Out-of-time-ordered correlators and purity in rational conformal field theories, Prog. Theor. Exp. Phys. 2016, 113B06 (2016).
  38. Alexander B. Zamolodchikov and Alexei B. Zamolodchikov, Liouville field theory on a pseudosphere, arXiv:hep-th/0101152.
  39. A. Liam Fitzpatrick and Jared Kaplan, On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles, J. High Energy Phys. 04 (2017) 072.
  40. Nadav Drukker, Davide Gaiotto, and Jaume Gomis, The virtue of defects in 4D gauge theories and 2D CFTs, J. High Energy Phys. 06 (2011) 025.
  41. Adel Bilal, Introduction to W algebras, in Proceedings of spring school on string theory and quantum gravity, Trieste, Italy, April 15–23 (World Scientific, Singapore, 1991).
  42. Peter Bouwknegt and Kareljan Schoutens, W symmetry in conformal field theory, Phys. Rep. 223, 183 (1993).
  43. Chethan Krishnan, Avinash Raju, Shubho Roy, and Somyadip Thakur, Higher spin cosmology, Phys. Rev. D 89, 045007 (2014).
  44. Kazuki Doi, Jonathan Harper, Ali Mollabashi, Tadashi Takayanagi, and Yusuke Taki, Pseudo Entropy in dS/CFT and Time-Like Entanglement Entropy, Phys. Rev. Lett. 130, 031601 (2023).
  45. K. Narayan, de Sitter space, extremal surfaces and “time-entanglement”, arXiv:2210.12963.
  46. K. Narayan, Extremal surfaces in de Sitter spacetime, Phys. Rev. D 91, 126011 (2015).
  47. Yoshiki Sato, Comments on entanglement entropy in the dS/CFT correspondence, Phys. Rev. D 91, 086009 (2015).
  48. Kazuki Doi, Jonathan Harper, Ali Mollabashi, Tadashi Takayanagi, and Yusuke Taki, Timelike entanglement entropy, arXiv:2302.11695.
  49. Andrea Campoleoni, Stefan Fredenhagen, and Joris Raeymaekers, Quantizing higher-spin gravity in free-field variables, J. High Energy Phys. 02 (2018) 126.
  50. David Simmons-Duffin, The conformal bootstrap, in New Frontiers in Fields and Strings (World Scientific, Singapore, 2017), pp. 1–74.
  51. David Poland, Slava Rychkov, and Alessandro Vichi, The conformal bootstrap: Theory, numerical techniques, and applications, Rev. Mod. Phys. 91, 015002 (2019).
  52. Dionysios Anninos, Thomas Hartman, and Andrew Strominger, Higher spin realization of the dS/CFT correspondence, Classical Quantum Gravity 34, 015009 (2017).

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Phys. Rev. D 107, L101902– Published 24 May, 2023
  • Received 28 February 2023
  • Accepted 10 May 2023
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