TY - JOUR

T1 - Gravitation from entanglement in holographic CFTs

AU - Faulkner, Thomas

AU - Guica, Monica

AU - Hartman, Thomas

AU - Myers, Robert C.

AU - Van Raamsdonk, Mark

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2014/3

Y1 - 2014/3

N2 - 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 = 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.

AB - 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 = 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.

KW - AdS-CFT Correspondence

KW - Gauge-gravity correspondence

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U2 - 10.1007/JHEP03(2014)051

DO - 10.1007/JHEP03(2014)051

M3 - Article

AN - SCOPUS:84896522876

VL - 2014

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 51

ER -