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Title: The holographic shape of entanglement and Einstein’s equations

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics, Dept. of Physics
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). David Rittenhouse Lab.

We study shape-deformations of the entanglement entropy and the modular Hamiltonian for an arbitrary subregion and state (with a smooth dual geometry) in a holographic conformal field theory. More precisely, we study a double-deformation comprising of a shape deformation together with a state deformation, where the latter corresponds to a small change in the bulk geometry. Using a purely gravitational identity from the Hollands-Iyer-Wald formalism together with the assumption of equality between bulk and boundary modular flows for the original, undeformed state and subregion, we rewrite a purely CFT expression for this double deformation of the entropy in terms of bulk gravitational variables and show that it precisely agrees with the Ryu-Takayanagi formula including quantum corrections. As a corollary, this gives a novel, CFT derivation of the JLMS formula for arbitrary subregions in the vacuum, without using the replica trick. Finally, we use our results to give an argument that if a general, asymptotically AdS spacetime satisfies the Ryu-Takayanagi formula for arbitrary subregions, then it must necessarily satisfy the non-linear Einstein equation.

Research Organization:
Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FG02-05ER41367
OSTI ID:
1507703
Journal Information:
Journal of High Energy Physics (Online), Vol. 2018, Issue 5; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 30 works
Citation information provided by
Web of Science

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Cited By (20)

The holographic dual of the entanglement wedge symplectic form journal January 2020
Nearly AdS2 holography in quantum CGHS model journal January 2020
Holographic excited states in AdS black holes journal April 2019
Towards bulk metric reconstruction from extremal area variations journal August 2019
Surface theory: the classical, the quantum, and the holographic journal September 2019
The holographic dual of the entanglement wedge symplectic form text January 2020
The holographic dual of the entanglement wedge symplectic form text January 2020
Towards Bulk Metric Reconstruction from Extremal Area Variations text January 2019
The Holographic Dual of the Entanglement Wedge Symplectic Form text January 2019
Nearly AdS$_2$ holography in quantum CGHS model text January 2019
Nearly AdS2 holography in quantum CGHS model journal January 2020
Surface theory: the classical, the quantum, and the holographic journal September 2019
More of the bulk from extremal area variations journal December 2020
The holographic dual of the entanglement wedge symplectic form text January 2020
Comments on black hole interiors and modular inclusions text January 2018
Second-order Lovelock Gravity from Entanglement in Conformal Field Theories text January 2019
Holographic scattering requires a connected entanglement wedge text January 2019
Modular Hamiltonians for Euclidean Path Integral States preprint January 2020
Endpoint contributions to excited-state modular Hamiltonians text January 2020
Bit threads, Einstein's equations and bulk locality text January 2020

Figures / Tables (3)


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