Gravitational dynamics from entanglement “thermodynamics”
By Nima Lashkari, Michael B. McDermott, Mark Van Raamsdonk. 2013
366 citations recorded by the source corpus.
A bstractIn 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0c29d7071db744d0dfaeb6d73124b764491cd719
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Citations in the corpus
- Gravitation from entanglement in holographic CFTs (2013, methodology): “The expression for δS grav B was taken from [7, 8].”
- Nonlinear gravity from entanglement in conformal field theories (2017, background): “In [8, 9], it was demonstrated that any spacetime geometry that correctly captures the entanglement entropy of a near-vacuum CFT state to first order in the perturbation must satisfy Einstein’s equations linearized about Anti de Sitter space.”
- Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, background): “This latter proposal, known as the RyuTakayanagi (RT) formula, has led to much further work on sharpening the connection between geometry and entanglement [5–12] In the condensed matter physics community, improved understanding of quantum entanglement has led to significant progress in the numerical”
- Bulk curves from boundary data in holography (2013, background): “Some relevant references include [47, 48, 49, 50]; see also [51] on the holographic emergence of Einstein’s equations.”
- A stereoscopic look into the bulk (2016, background): “• a new construction for local bulk operators [12–19]; • a novel look at the modular Hamiltonian [7]; • the origin of geodesic Witten diagrams and their use in computing conformal blocks [20–22]; • and a re-derivation of Einstein’s equations from entanglement (along the lines of [23–25]), whose deta”
- Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “This framework naturally allow us to derive the integrated equations of motion by assuming that the entanglement entropy is given by the area thus generalizing [16, 17].”
- Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
- Remarks on the necessity and implications of state-dependence in the black hole interior (2015, methodology): “2 Equations of motion from the first law of entanglement Another approach of deriving the bulk from the boundary, which has attracted attention, is the program of deriving the bulk equations of motion from the “first law of entanglement” [29, 30, 31].”
- Universality of Gravity from Entanglement (2014, methodology): “In [13, 14], it was shown using the leading order RT formula for holographic entanglement entropy that the general CFT result Eq.”