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Cited by 1,822Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesQuantum Electrodynamics and Casimir Effect

A covariant holographic entanglement entropy proposal

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Hubeny, Veronika E, Rangamani, Mukund, Takayanagi, Tadashi·2007·Journal of High Energy Physics
DOI 10.1088/1126-6708/2007/07/062
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Crossref · 10.1088/1126-6708/2007/07/062

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  • The Ryu-Takayanagi formula, including quantum corrections, states that the entanglement entropy of a boundary region B is equal to the generalised entropy of the Ryu-Takayanagi surface.

    “The Ryu-Takayanagi formula, including quantum corrections, states that entanglement entropy of the boundary region B is equal to the generalised entropy of the Ryu-Takayanagi surface.”

    From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [28]

    The discussion around eq. (2.2) gives the boundary region’s entanglement entropy as the area of a bulk minimal surface divided by 4G. The paper also discusses quantum corrections to a Bousso entropy bound around eqs. (3.4)–(3.5), but it does not state that the quantum-corrected boundary entropy equals the generalised entropy of an RT surface. The passages in our copy have no page numbers. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • In this way, we obtain the quantum extremal surface prescription of [23], and also [20, 21].

    “In this way, we obtain the quantum extremal surface prescription of [23], and also [20, 21].”

    From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [21]

    Section 3.3, equation (3.15), proposes calculating holographic entanglement entropy from the area of a surface with vanishing null expansions. That supports an extremal-surface prescription, but the passage does not give the quantum extremal-surface prescription claimed here: it extremizes area, not a quantity including bulk entropy. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • The entropy of the black hole is given by the generalized entropy of the quantum extremal surface (QES), a quantum-corrected Ryu-Takayanagi surface.

    “The entropy of the black hole is given by the generalized entropy of the quantum extremal surface (QES) [23], which is a quantum-corrected Ryu-Takayanagi (or Hubeny-Rangamani-Takayanagi) surface [20, 21].”

    From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [21]

    Section 3.3 describes the covariant extremal-surface prescription, supporting the identification of an HRT surface. Section 6.6 relates that surface to the apparent horizon in a limiting case. The cited paper does not state that a quantum extremal surface is obtained by extremizing generalized entropy; the citing sentence assigns the QES entropy claim to a different citation. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The QRT prescription for entanglement entropy between A and its complement is given by the smallest extremal value of the generalized entropy.

    “The QRT prescription for entanglement entropy between A and ¯ A , or in this case the entanglement entropy between the black hole and the Hawking radiation, is then given by the smallest extremal value of (2.1).”

    From Page curve for an evaporating black hole (2020) · cites this paper as [8]

    Section 3.3, proposal (II) (page not provided), says to choose the minimum-area surface when multiple extremal surfaces satisfy the boundary and homotopy conditions. It gives entropy as area divided by 4G, not as the extremal value of generalized entropy, and does not state this prescription for entanglement between a black hole and its Hawking radiation. (LLM, conf=0.89)

    Experimental — accuracy not yet measured

  • The Ryu-Takayanagi or covariant Hubeny-Rangamani-Takayanagi prescription computes the entanglement entropy of a spacelike region A in the CFT in the bulk by the area of a codimension-two minimal surface with boundary anchored on the boundary of A.

    “This can be explicitly checked with the Ryu-Takayanagi (RT) or the covariant Hubeny-Rangamani-Takayanagi prescription (Ryu and Takayanagi, 2006a,b;Hubeny et al., 2007): The entanglement entropy of a spacelike region A in the CFT is computed in the bulk by the area of a codimension-two minimal surface with boundary anchored on ∂A.”

    From Euclidean Wormholes, Baby Universes, and Their Impact on Particle Physics and Cosmology (2018) · cites this paper as Hubeny et al., 2007

    The paper’s static prescription describes entanglement entropy using the area of a codimension-two minimal bulk surface anchored on ∂A. Its covariant proposal (section 3.3, equation 3.15; page unavailable) instead uses an extremal surface with vanishing null expansions, choosing the minimum-area surface only among qualifying extremal surfaces. Calling the covariant surface simply a minimal surface omits that distinction. (LLM, conf=0.90)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 12

  1. [5]5. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) 2 [hep-th/0405152]. · arXiv
  2. [13]13. M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, cond-mat/0510613. · arXiv
  3. [17]17. D. Bigatti and L. Susskind, TASI lectures on the holographic principle, hep-th/0002044. · arXiv
  4. [24]24. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001]. · arXiv
  5. [26]26. M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, arXiv:0704.3719. · arXiv
  6. [29]29. S.N. Solodukhin, Entanglement entropy of black holes and AdS/CFT correspondence, Phys. Rev. Lett. 97 (2006) 201601 [hep-th/0606205]. · arXiv
  7. [32]32. J.-W. Lee, J. Lee and H.-C. Kim, Dark energy from vacuum entanglement, hep-th/0701199. · arXiv
  8. [33]33. M. Cadoni, Entanglement entropy of two-dimensional Anti-de Sitter black holes, arXiv:0704.0140. · arXiv
  9. [46]46. S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge (1973).
  10. [54]54. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein's field equations, Cambridge Univ. Pr., Cambridge (2003).
  11. [56]56. V. Balasubramanian et al., Typicality versus thermality: an analytic distinction, hep-th/0701122. · arXiv
  12. [63]63. J. Hammersley, Numerical metric extraction in AdS/CFT, arXiv:0705.0159. · arXiv

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Authors
Hubeny, V. E., Rangamani, M., & Takayanagi, T.
Affiliations
  • Durham University (GB)
  • Kyoto University (JP)
ORCID
Hubeny, Veronika E
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2007-07-23
Volume
2007
Issue
07
Pages
062-062
ISSN
1029-8479 (ISSN-L)
DOI
10.1088/1126-6708/2007/07/062
OpenAlex
W2157692768
Cited by
1,822
References
50
Citations by year
2026: 79 · 2025: 151 · 2024: 145 · 2023: 183 · 2022: 182 · 2021: 195 · 2020: 179 · 2019: 144 · 2018: 115 · 2017: 91 · 2016: 112 · 2015: 74 · 2014: 73 · 2013: 36 · 2012: 18
FWCI
6.12
Type
journal article
Language
en
Open access
Locations
  • Journal of High Energy Physics (publishedVersion)
  • Durham Research Online (Durham University) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Durham Research Online (Durham University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • Japan Society for the Promotion of Science (19GS0219)
  • Kavli Institute for Theoretical Physics, University of California, Santa Barbara
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
Keywords
holographic entanglement entropy, covariant entropy bound, light sheet, AdS/CFT correspondence, Euclidean wormholes

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