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Cited by 520Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesRelativity and Gravitational Theory

Gravitation from entanglement in holographic CFTs

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Faulkner, Thomas, Guica, Monica, Hartman, Thomas, Myers, Robert C., Van Raamsdonk, Mark·2014·Journal of High Energy Physics
DOI 10.1007/jhep03(2014)051
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Abstract

Entanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S = $ \mathcal{A} $ /(4G N), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

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  • Sarosi and Ugajin show that their construction relates the quantum Fisher information to the canonical energy of an emergent bulk for any CFT without assuming either the RT/HRT formula in the bulk or the large N limit for the CFT.

    “Sarosi and Ugajin [133] show using the results of [118] (valid for the Rindler wedge) that their construction of the modular Hamiltonian relates the quantum Fisher information to the canonical energy of an emergent bulk for any CFT without assuming either the RT/HRT formula in the bulk or the large N limit for the CFT.”

    From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [118]

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Authors
Faulkner, T., Guica, M., Hartman, T., Myers, R. C., & Van Raamsdonk, M.
Affiliations
  • Institute for Advanced Study (US)
  • University of Pennsylvania (US)
  • University of California, Santa Barbara (US)
  • Perimeter Institute (CA)
Corresponding author
Guica, Monica
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2014-03
Volume
2014
Issue
3
ISSN
1029-8479 (ISSN-L)
DOI
10.1007/jhep03(2014)051
OpenAlex
W2102970467
Cited by
520
References
5
Citations by year
2026: 29 · 2025: 29 · 2024: 12 · 2023: 38 · 2022: 36 · 2021: 42 · 2020: 54 · 2019: 48 · 2018: 49 · 2017: 53 · 2016: 55 · 2015: 39 · 2014: 35
FWCI
26.75
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Journal of High Energy Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (No.NSF PHY11-25915, PHY11- 25915, NSF PHY-11-25915, 25915)
  • Canadian Institute for Advanced Research
  • Government of Canada
  • Industry Canada
  • Institut Périmètre de physique théorique
  • Natural Sciences and Engineering Research Council of Canada
  • Kavli Institute for Theoretical Physics, University of California, Santa Barbara (PHY-11-25915, NSF PHY11-25915)
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 › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
entanglement entropy, first law of thermodynamics, holographic CFT, Ryu-Takayanagi formula, linearized Einstein equations, higher-curvature gravity, Wald entropy, AdS/CFT correspondence, holographic stress tensor, holographic renormalization, quantum gravity, AdS spacetime

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