The holographic shape of entanglement and Einstein’s equations
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics, Dept. of Physics
- 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
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