Skip to main content

Advertisement

SpringerLink
  • Journal of High Energy Physics
  • Journal Aims and Scope
  • Submit to this journal
De Sitter holography and entanglement entropy
Download PDF
Your article has downloaded

Similar articles being viewed by others

Slider with three articles shown per slide. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide.

Holographic entanglement entropy is cutoff-covariant

03 October 2019

Jonathan Sorce

Gravitation in flat spacetime from entanglement

06 December 2019

Victor Godet & Charles Marteau

Renormalized holographic entanglement entropy in Lovelock gravity

11 June 2021

Giorgos Anastasiou, Ignacio J. Araya, … Rodrigo Olea

Holographic entanglement and Poincaré blocks in three-dimensional flat space

10 May 2018

Eliot Hijano & Charles Rabideau

Holo-ween

04 December 2020

Petar Simidzija & Mark Van Raamsdonk

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled

03 September 2018

Aurelio Romero-Bermúdez, Philippe Sabella-Garnier & Koenraad Schalm

Lifshitz entanglement entropy from holographic cMERA

02 July 2018

Simon A. Gentle & Stefan Vandoren

Reflected entropy in double holography

04 February 2022

Yi Ling, Peng Liu, … Cheng-Yong Zhang

Swing surfaces and holographic entanglement beyond AdS/CFT

10 December 2020

Luis Apolo, Hongliang Jiang, … Yuan Zhong

Download PDF
  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 09 July 2018

De Sitter holography and entanglement entropy

  • Xi Dong  ORCID: orcid.org/0000-0001-7048-34641,
  • Eva Silverstein2 &
  • Gonzalo Torroba3 

Journal of High Energy Physics volume 2018, Article number: 50 (2018) Cite this article

  • 1260 Accesses

  • 55 Citations

  • 21 Altmetric

  • Metrics details

A preprint version of the article is available at arXiv.

Abstract

We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d + 1 dimensions involves two coupled CFT sectors constrained by residual d-dimensional gravity. In the d = 2 case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large central charge and a sparse light spectrum, derived by Hartman, Keller, and Stoica. Significant interactions between the two CFTs, derived previously for other reasons, suggest a maximally mixed state upon tracing out one of the two sectors; we derive this by determining the holographic Renyi entropies. The resulting entanglement entropy matches the Gibbons-Hawking formula for de Sitter entropy, including the numerical coefficient. Finally, we interpret the Gibbons-Hawking horizon entropy in terms of the Ryu-Takayanagi entropy, and explore the time evolution of the entanglement entropy.

Download to read the full article text

Working on a manuscript?

Avoid the most common mistakes and prepare your manuscript for journal editors.

Learn more

References

  1. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  3. X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  4. J. Camps, Generalized entropy and higher derivative Gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  6. M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [INSPIRE].

  7. J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].

  8. S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  9. P. Gao, D.L. Jafferis and A. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].

  12. V. Balasubramanian, M.B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86 (2012) 045014 [arXiv:1108.3568] [INSPIRE].

    ADS  Google Scholar 

  13. A. Mollabashi, N. Shiba and T. Takayanagi, Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy, JHEP 04 (2014) 185 [arXiv:1403.1393] [INSPIRE].

    Article  ADS  Google Scholar 

  14. M.R. Mohammadi Mozaffar and A. Mollabashi, On the Entanglement Between Interacting Scalar Field Theories, JHEP 03 (2016) 015 [arXiv:1509.03829] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. M.R. Mohammadi Mozaffar and A. Mollabashi, Entanglement in Lifshitz-type Quantum Field Theories, JHEP 07 (2017) 120 [arXiv:1705.00483] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. A. Karch and C.F. Uhlemann, Holographic entanglement entropy and the internal space, Phys. Rev. D 91 (2015) 086005 [arXiv:1501.00003] [INSPIRE].

    ADS  Google Scholar 

  17. G.W. Gibbons and S.W. Hawking, Cosmological Event Horizons, Thermodynamics and Particle Creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  18. X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. M. Alishahiha, A. Karch and E. Silverstein, Hologravity, JHEP 06 (2005) 028 [hep-th/0504056] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  22. M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2005) 393 [hep-th/0407125] [INSPIRE].

    Article  ADS  Google Scholar 

  23. X. Dong, B. Horn, S. Matsuura, E. Silverstein and G. Torroba, FRW solutions and holography from uplifted AdS/CFT, Phys. Rev. D 85 (2012) 104035 [arXiv:1108.5732] [INSPIRE].

    ADS  Google Scholar 

  24. B. Freivogel, Y. Sekino, L. Susskind and C.-P. Yeh, A holographic framework for eternal inflation, Phys. Rev. D 74 (2006) 086003 [hep-th/0606204] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  25. E. Silverstein, TASI lectures on cosmological observables and string theory, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015): Boulder, CO, U.S.A., June 1–26, 2015, pp. 545–606, 2017, arXiv:1606.03640 [INSPIRE].

  26. D. Anninos, de Sitter Musings, Int. J. Mod. Phys. A 27 (2012) 1230013 [arXiv:1205.3855] [INSPIRE].

  27. L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. X. Dong, B. Horn, E. Silverstein and G. Torroba, Moduli Stabilization and the Holographic RG for AdS and dS, JHEP 06 (2013) 089 [arXiv:1209.5392] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  29. D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].

  30. J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].

  31. A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].

  32. S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  33. W. Cottrell and A. Hashimoto, Comments on \( T\overline{T} \) double trace deformations and boundary conditions, arXiv:1801.09708 [INSPIRE].

  34. J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as a stochastic process, arXiv:1801.06895 [INSPIRE].

  35. P. Kraus, J. Liu and D. Marolf, Cutoff AdS 3 versus the \( T\overline{T} \) deformation, arXiv:1801.02714 [INSPIRE].

  36. L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].

  37. S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Generating small numbers by tunneling in multithroat compactifications, Int. J. Mod. Phys. A 19 (2004) 2657 [hep-th/0106128] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  38. S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Small numbers from tunneling between brane throats, Phys. Rev. D 64 (2001) 121702 [hep-th/0104239] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  39. T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. C.A. Keller and A. Maloney, Poincaré Series, 3D Gravity and CFT Spectroscopy, JHEP 02 (2015) 080 [arXiv:1407.6008] [INSPIRE].

  41. S. Hellerman, A Universal Inequality for CFT and Quantum Gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. N. Benjamin, M.C.N. Cheng, S. Kachru, G.W. Moore and N.M. Paquette, Elliptic Genera and 3d Gravity, Annales Henri Poincaré 17 (2016) 2623 [arXiv:1503.04800] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. T. Banks, Cosmological breaking of supersymmetry?, Int. J. Mod. Phys. A 16 (2001) 910 [hep-th/0007146] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. R. Bousso, Positive vacuum energy and the N bound, JHEP 11 (2000) 038 [hep-th/0010252] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. K. Narayan, On extremal surfaces and de Sitter entropy, Phys. Lett. B 779 (2018) 214 [arXiv:1711.01107] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  46. A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].

    Article  ADS  Google Scholar 

  48. Y. Nomura, P. Rath and N. Salzetta, Spacetime from Unentanglement, Phys. Rev. D 97 (2018) 106010 [arXiv:1711.05263] [INSPIRE].

  49. L. Susskind and E. Witten, The holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].

  50. M. Miyaji and T. Takayanagi, Surface/State Correspondence as a Generalized Holography, PTEP 2015 (2015) 073B03 [arXiv:1503.03542] [INSPIRE].

  51. Y. Sato, Comments on Entanglement Entropy in the dS/CFT Correspondence, Phys. Rev. D 91 (2015) 086009 [arXiv:1501.04903] [INSPIRE].

  52. K. Narayan, Extremal surfaces in de Sitter spacetime, Phys. Rev. D 91 (2015) 126011 [arXiv:1501.03019] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  53. S. Fischetti and D. Marolf, Complex Entangling Surfaces for AdS and Lifshitz Black Holes?, Class. Quant. Grav. 31 (2014) 214005 [arXiv:1407.2900] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  55. M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].

    ADS  Google Scholar 

  56. F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence, JHEP 06 (2015) 149 [arXiv:1503.06237] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter and Z. Yang, Holographic duality from random tensor networks, JHEP 11 (2016) 009 [arXiv:1601.01694] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  58. A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. X. Dong, D. Harlow and D. Marolf, to appear.

  60. R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. J. Polchinski, A Two-Dimensional Model for Quantum Gravity, Nucl. Phys. B 324 (1989) 123 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  62. A.R. Cooper, L. Susskind and L. Thorlacius, Two-dimensional quantum cosmology, Nucl. Phys. B 363 (1991) 132 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  63. B. Carneiro da Cunha and E.J. Martinec, Closed string tachyon condensation and world sheet inflation, Phys. Rev. D 68 (2003) 063502 [hep-th/0303087] [INSPIRE].

    ADS  Google Scholar 

  64. M. Dodelson, E. Silverstein and G. Torroba, Varying dilaton as a tracer of classical string interactions, Phys. Rev. D 96 (2017) 066011 [arXiv:1704.02625] [INSPIRE].

    ADS  Google Scholar 

  65. M.M. Wolf, F. Verstraete, M.B. Hastings and J.I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations, Phys. Rev. Lett. 100 (2008) 070502 [arXiv:0704.3906] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    Xi Dong

  2. Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA, 94306, U.S.A.

    Eva Silverstein

  3. Centro Atómico Bariloche and CONICET, Bariloche, Argentina

    Gonzalo Torroba

Authors
  1. Xi Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eva Silverstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gonzalo Torroba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xi Dong.

Additional information

ArXiv ePrint: 1804.08623

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dong, X., Silverstein, E. & Torroba, G. De Sitter holography and entanglement entropy. J. High Energ. Phys. 2018, 50 (2018). https://doi.org/10.1007/JHEP07(2018)050

Download citation

  • Received: 13 June 2018

  • Accepted: 29 June 2018

  • Published: 09 July 2018

  • DOI: https://doi.org/10.1007/JHEP07(2018)050

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Gauge-gravity correspondence
  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Black Holes
Download PDF

Working on a manuscript?

Avoid the most common mistakes and prepare your manuscript for journal editors.

Learn more

Advertisement

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • California Privacy Statement
  • How we use cookies
  • Manage cookies/Do not sell my data
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.