Gravitational Dynamics From Entanglement "Thermodynamics"

Abstract

In a general conformal field theory, perturbations to the vacuum state obey the relation δS = δE, where δS is the change in entanglement entropy of an arbitrary ball-shaped region, and δE is the change in "hyperbolic" energy of this region. In this note, we show that for holographic conformal field theories, this relation, together with the holographic connection between entanglement entropies and areas of extremal surfaces and the standard connection between the field theory stress tensor and the boundary behavior of the metric, implies that geometry dual to the perturbed state satisfies Einstein's equations expanded to linear order about pure AdS.

v2: references added, problematic section on Radon transform removed

References in corpus (7)

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• Relative Entropy and Holography
• Entanglement Temperature and Entanglement Entropy of Excited States
• Dynamics of Entanglement Entropy from Einstein Equation
• Entanglement Thermodynamics
• Entanglement Thermodynamics

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