Holographic entanglement beyond classical gravity

By Taylor Barrella, Xi Dong, S. Hartnoll, Victoria L. Martin. 2013

241 citations recorded by the source corpus.

A bstractThe Rényi entropies and entanglement entropy of 1+1 CFTs with gravity duals can be computed by explicit construction of the bulk spacetimes dual to branched covers of the boundary geometry. At the classical level in the bulk this has recently been shown to reproduce the conjectured Ryu-Takayanagi formula for the holographic entanglement entropy. We study the one-loop bulk corrections to this formula. The functional determinants in the bulk geometries are given by a sum over certain words of generators of the Schottky group of the branched cover. For the case of two disjoint intervals on a line we obtain analytic answers for the one-loop entanglement entropy in an expansion in small cross-ratio. These reproduce and go beyond anticipated universal terms that are not visible classically in the bulk. We also consider the case of a single interval on a circle at finite temperature. At high temperatures we show that the one-loop contributions introduce expected finite size corrections to the entanglement entropy that are not present classically. At low temperatures, the one-loop corrections capture the mixed nature of the density matrix, also not visible classically below the Hawking-Page temperature.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91b8c39f181fb307e00618685e8cafec94ba0902

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Citations in the corpus

Relative entropy equals bulk relative entropy (2015, unknown): “A leading order holographic prescription for computing entanglement entropy was proposed in [21, 22] and it was extended to the next order in GN in [23] (see also [24]).”
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy (2012, background): “In this regime, it is known that the holographic entropy must be modified to include a term proportional to the bulk entanglement entropy [48–50].”
Entropy, extremality, euclidean variations, and the equations of motion (2017, unknown): “4) agrees with the one-loop result of [21, 22] and was conjectured (1)For Einstein gravity, Agen = A 4GN .”
Gravitation from entanglement in holographic CFTs (2013, background): “Thus, the first law should place constraints on the quantum behaviour of the bulk gravitational theory and will likely also involve an understanding of the quantum corrections to the Ryu-Takayanagi formula as discussed recently in [59–61].”
Traversable wormholes via a double trace deformation (2016, background): “4 Holographic Energy and Entropy In this section we will consider the implications of a traversable wormhole for the holographic entanglement entropy conjecture, which in this context relates the entanglement entropy between the two boundary CFT’s to the area/entropy of certain extremal surfaces in ”
Black hole collapse in the 1/c expansion (2016, methodology): “Recently, these methods have been recast and extended to a set of general techniques for computing observables in large-c conformal field theory, without reference to a particular Lagrangian or other microscopic details [8–11].”
Holographic entanglement entropy for general higher derivative gravity (2013, background): “nd proven by Lewkowycz and Maldacena [7]. Proof of the formula for special cases includes [6,14,15]. Earlier attempts to prove the formula include [16,17]. One-loop corrections { 4 { were analyzed in [18,19]. A covariant version of the prescription which applies in general time-dependent cases was p”
Quantum corrections to holographic entanglement entropy (2013, methodology): “Similarly, if we compute the quantum correction using the replica trick, we can just compute the determinants, and analytically continue them without worrying about the changes in the classical background due to the quantum corrections, as was done for AdS3 in [16].”
Notes on islands in asymptotically flat 2d dilaton black holes (2020, background): “The second term is the bulk entanglement entropy, which is the quantum corrections of RT formula [11, 12].”
Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, methodology): “The first quantum corrections to this formula were computed, at order O(N0) (boundary) or O(~0) (bulk), by Faulkner, Lewkowycz, and Maldacena (FLM); see also [42, 43].”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “…within the pure gravitational theory, loop corrections to Renyi entropies on the gravity side are reproduced by conformal blocks including not just Virasoro descendants of the vacuum but also additional descendants that arise from acting with operators from the di(cid:11)erent \replicas" [32, 33].”
The holographic entropy cone (2015, unknown): “, [44, 45]).”
Islands in cosmology (2020, background): “The island rule is a generalized version of the Ryu-Takayanagi formula for holographic entanglement entropy [17,40–44].”
Universal spectrum of 2d conformal field theory in the large c limit (2014, result): “This is similar in spirit to recent efforts to derive universal features of entanglement entropy [12, 13, 14, 15] and gravitational interactions [16] at large c.”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, unknown): “If ρ is “appropriate” then the von Neumann entropy of ρA is given by [20], [19, 21–23]”
Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, methodology): “The full Renyi entropy in a thermal state cannot equal the Renyi entropy in a pure state, since the former is not invariant under `→ 2π − ` [10].”