Deriving covariant holographic entanglement

By Xi Dong, Aitor Lewkowycz, M. Rangamani. 2016

293 citations recorded by the source corpus.

A bstractWe provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b77011b3ad0c4bcf4cba89205f10c281bd9b8ab1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. D. Harlow
2. D. Stanford
3. S. Shenker
4. R. Myers
5. Zhenbin Yang
6. Ahmed Almheiri
7. Thomas Hartman
8. Henry Maxfield

In Nuclear and High Energy Physics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. S. Raju
5. J. Maldacena
6. Thomas Hartman
7. S. Shenker
8. Zhenbin Yang

In Statistical and Nonlinear Physics

1. D. Harlow
2. D. Stanford
3. R. Myers
4. S. Raju
5. Thomas Hartman
6. S. Shenker
7. J. Maldacena
8. H. Chen

Citations in the corpus

• Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “e boundary region R, and GN denotes Newton’s constant. This prescription for holographic entanglement entropy was derived from AdS/CFT in [9]. Furthermore, it is valid in general time-dependent cases [10, 11]. In general, the gravitational theory in the bulk is described at low energies in terms of ”
• Comments on holographic complexity (2016, background): “A natural extension of this prescription to a time-dependent bulk spacetime refers to the Hubeny-Rangamani-Takayanagi (HRT) prescription for holographic entanglement entropy [36] (see also [37]) as follows:7”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “the bulk and does not serve as a boundary of spacetime. We emphasize that here this discussion implicitly relies on the standard derivation of the RT prescription for holographic entanglement entropy [123,124] in the bulk perspective, where again we assume that there is no ensemble averaging.50 Foll”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, methodology): “The stationary classical version of the correspondence was given a reasonably precise derivation in [74], which was covariantized in [76], and which was extended to include quantum corrections in [8, 75].”
• Replica wormholes and the black hole interior (2019, methodology): “Since the Ryu-Takayanagi formula can be derived from gravitational path integrals using replicas [7, 8, 9, 23], the prescription (1.”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “Following [93, 111], the same applies for general time dependent situations.”
• On entanglement spreading in chaotic systems (2016, background): “At this time, the geometry that the HRT surface is experiencing is that of a static black hole.”
• Islands in asymptotically flat 2D gravity (2020, methodology): “local analysis closely follows the derivation of the Ryu-Takayanagi formula by Lewkoywycz and Maldacena [56] and the general analysis of quantum extremal surfaces by Dong and Lewkowycz [57] (see also [58]). By assuming a large-Nmatter sector, we sidestep some of the diculties in dening the matter en”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “upled to Op1qbulk quantum elds may be written S gen ApXq 4G N S bulkpXq, where S bulkpXqis a von Neumann entropy of bulk quantum elds on one side of X. As explained in [15] and partially veried in [13], this means that bulk quantum eects should move the boundary of W A to a so-called quantum extrem”
• Islands in Schwarzschild black holes (2020, background): “1) consists of two terms; the gravitational part3 of the generalized entropy, Sgravity, which is proportional to the total area (or volume for D > 4) of the boundaries of an island, ∂I, as [30–33]”