Gravitational dynamics from entanglement “thermodynamics”

A bstract In a general conformal field theory, perturbations to the vacuum state obey the relation δ S = δ E , where δ S is the change in entanglement entropy of an arbitrary ball-shaped region, and δ E is the change in “hyperbolic” energy of this region. In this note, we show that for holographic c...

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Bibliographic Details
Published in:The journal of high energy physics 2014-04, Vol.2014 (4), p.1-16, Article 195
Main Authors: Lashkari, Nima, McDermott, Michael B., Van Raamsdonk, Mark
Format: Article
Language:English
Subjects:
Boundaries
Classical and Quantum Gravitation
Einstein equations
Elementary Particles
Entanglement
Entropy
Field theory
Gravitation
High energy physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Stress tensors
String Theory
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Summary:A bstract In a general conformal field theory, perturbations to the vacuum state obey the relation δ S = δ E , where δ S is the change in entanglement entropy of an arbitrary ball-shaped region, and δ E 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2014)195