Nonlinear constraints on gravity from entanglement

Abstract

Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We show that the Einstein value satisfies the positivity condition while the multi-dimensional parameter space away from it gets constrained.

31 pages, 4 figures, to appear in CQG

References in corpus (13)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Generalized gravitational entropy
• Gravitation from Entanglement in Holographic CFTs
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Relative Entropy and Holography
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• Thermodynamical Property of Entanglement Entropy for Excited States
• Generalized entropy and higher derivative Gravity
• On generalized gravitational entropy, squashed cones and holography
• Entanglement entropy in higher derivative holography
• Entropic Counterpart of Perturbative Einstein Equation
• Constraining gravity using entanglement in AdS/CFT

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• Tomography from Entanglement
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• The holographic entropy zoo
• Quantum tasks in holography
• Positive gravitational subsystem energies from CFT cone relative entropies
• The holographic dual of Rényi relative entropy
• Strong subadditivity and holography