Holographic entanglement entropy for general higher derivative gravity

By Xi Dong. 2013

477 citations recorded by the source corpus.

A bstractWe propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula consists of Wald’s formula for the black hole entropy, as well as corrections involving the extrinsic curvature. We derive these corrections by noting that they arise from naively higher order contributions to the action which are enhanced due to would-be logarithmic divergences. Our formula reproduces the Jacobson-Myers entropy in the context of Lovelock gravity, and agrees with existing results for general four-derivative gravity.We emphasize that the formula should be evaluated on a particular bulk surface whose location can in principle be determined by solving the equations of motion with conical boundary conditions. This may be difficult in practice, and an alternative method is desirable. A natural prescription is simply minimizing our formula, analogous to the Ryu-Takayanagi prescription for Einstein gravity. We show that this is correct in several examples including Lovelock and general four-derivative gravity.

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

View Paper: https://www.semanticscholar.org/paper/a3e719a15199a8b305e946c8a518e23dbc023d00

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. V. Hubeny
4. T. Faulkner
5. M. Rangamani
6. D. Stanford
7. T. Takayanagi
8. S. Raju

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

1. D. Harlow
2. R. Myers
3. S. Raju
4. Aitor Lewkowycz
5. D. Stanford
6. T. Faulkner
7. Thomas Hartman
8. Aron C. Wall

Citations in the corpus

• Geometric entropy and edge modes of the electromagnetic field (2015, methodology): “This ambiguity was recently resolved for the case of classical higher derivative gravity [28, 29] and when applied to the case of classical Maxwell theory, this refinement of Wald’s formula gives zero [26, 30].”
• Deriving covariant holographic entanglement (2016, methodology): “For simplicity we will consider Einstein-Hilbert gravity here; generalizations to other classical gravitational theories follow along the lines of [23, 24].”
• Integral geometry and holography (2015, background): “We could also consider alternate entropy functionals for higher-derivative gravity [54].”
• Gravitation from entanglement in holographic CFTs (2013, background): “, [1, 2, 25, 32–38]), it is given by extremizing a certain functional of the bulk metric over codimension-two bulk surfaces whose boundary coincides with ∂A in the boundary CFT.”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, methodology): “The RT/HRT conjecture has also recently been extended to bulk theories more general than Einstein gravity [136], and it also has been used to derive formulae for the areas of more general non-extremal bulk surfaces [137, 138].”
• Causality & holographic entanglement entropy (2014, background): “When the higher-derivative operators are unsuppressed we have little to say for two reasons: (a) the holographic entanglement prescription so far is only given for static situations (or with time reversal symmetry) [43, 44] and (b) even assuming the covariant generalizations, one is stymied by the a”
• Mutual information and the F-theorem (2015, background): “in [68]. We might add that eq. (A.1) assumes that the bulk theory corresponds to Einstein gravity and this expression has been extended to certain higher curvature theories as well [67,69] | see also [70]. Let us also note here that mutual information was discussed in a holographic context by [66,71”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “Here LA denotes a particular local operator in the bulk integrated over γA: at leading order in Newton’s constant G we have LA = Area(γA) 4G , while at higher orders, both in G but also in other couplings such as α′, there are corrections to LA involving various intrisic and extrinsic quantities int”
• Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, methodology): “This would produce additional subleading highercurvature corrections to Sgen, which can be calculated for actions which are arbitrary functions of the Riemann tensor by using the Dong entropy formula [37].”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “In such contexts one should also consider corrections to the classical formula A 4GN associated with higher derivative corrections to the gravitational effective action [16–20].”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, methodology): “• Since the Ryu-Takayanagi formula has been independently established using the replica trick methodology of [74, 76, 8, 75], theorem (5.”