Generalized gravitational entropy

By Aitor Lewkowycz, J. Maldacena. 2013

1,316 citations recorded by the source corpus.

A bstractWe consider classical Euclidean gravity solutions with a boundary. The boundary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector.A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.

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

View Paper: https://www.semanticscholar.org/paper/2cc91beee70a49b0c3e33c4fe562f571346caff7

How researchers see this paper

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

In Astronomy and Astrophysics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. S. Raju
5. J. Maldacena
6. T. Takayanagi
7. V. Hubeny
8. Thomas Hartman

In Nuclear and High Energy Physics

1. D. Harlow
2. R. Myers
3. S. Raju
4. J. Maldacena
5. D. Stanford
6. T. Takayanagi
7. Thomas Hartman
8. V. Hubeny

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. R. Myers
4. D. Stanford
5. J. Maldacena
6. Thomas Hartman
7. V. Hubeny
8. T. Faulkner

Citations in the corpus

• Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, background): “The geometric entanglement entropy in the CFT is related to the bulk through the holographic entanglement entropy proposal [13–15].”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “If N = 0, then it was shown [9] that a δnφ change cannot cancel the singularity of ∂δρ = (n−1) z , so one concludes that ∂φ = 0.”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “Indeed last year a fairly general “heuristic proof” was given by Lewkowycz and Maldacena [94], although the range of validity of this argument is still being actively explored by the community.”
• Holographic entanglement beyond classical gravity (2013, background): “The Ryu-Takayanagi proposal has very recently been proven in detail for certain 1+1 dimensional conformal field theories with large central charge [4, 5], while strong arguments for its validity in higher dimensions have also been presented [6].”
• 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]”
• Multiboundary wormholes and holographic entanglement (2014, background): “k spacetime which is homologous to A. As evidence in its favor, this generalization has been shown to satisfy strong subadditivity [52]. In addition, while it may be dicult to extend the argument of [7] to the case of fully general time-dependence, the extension to subregions of the time-re ection i”
• Holographic entanglement entropy for general higher derivative gravity (2013, methodology): “ase where it is a Killing horizon, our argument can be thought of as a holographic derivation of Wald’s formula. We begin in Section2with a review on the derivation of the Ryu-Takayanagi prescription [7], rephrasing it sometimes for our later generalization beyond Einstein gravity. In Section3, we d”
• Relative entropy and holography (2013, background): “However, a derivation was provided for the special case of a spherical entangling surface in [20] and quite remarkably, [21] recently extended this derivation to general (smooth) entangling surfaces.”
• A general proof of the quantum null energy condition (2017, background): “lar this means that ‘ j will stay an integer under n-analytic continuation, ruling out things like ‘ j=? pnfor p2Z. All of these requirements are actually in line with the n continuation advocated in [71,83] for computing holographic Renyi entropies. With this in mind an appropriate continuation wou”
• 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].”
• Causality & holographic entanglement entropy (2014, methodology): “In this case we have a lot of confidence in this entry to the AdS/CFT dictionary; firstly the RT formula obeys rather non-trivial general properties of entanglement entropies such as strong subadditivity [8–10], and secondly a general argument has been given for it in the context of Euclidean quantu”
• Entanglement entropy and nonabelian gauge symmetry (2014, methodology): “Arguments for the conjecture make use of the Euclidean replica trick formula for the entanglement entropy [6, 9, 10, 11, 12, 13], and so are only indirectly related to the canonical formula (2).”
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, background): “Compelling evidence in support of RT’s conjecture continues to accumulate [25], including rigorous proofs for d = 2 [26,27].”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “Key steps in the above arguments rely on identifying the area A of the HRT surface as 4GN times the von Neumann entropy of the field theory degrees of freedom in A [4, 10–13].”