On holographic entanglement entropy and higher curvature gravity

By Ling-Yan Hung, R. Myers, M. Smolkin. 2011

333 citations recorded by the source corpus.

We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald’s formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT’s in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.

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

View Paper: https://www.semanticscholar.org/paper/c573da8b0e0f5f6176cf0995ee5a2e818f332f2d

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Citations in the corpus

Gravitation from entanglement in holographic CFTs (2013, background): “In general, the entanglement entropy functional is known to differ from the Wald functional [21, 23] by terms quadratic in the extrinsic curvature of the extremal bulk surface.”
On volumes of subregions in holography and complexity (2016, background): “Similar to the case of entanglement entropy [13, 14], in [44] this divergence structure is written in terms of the curvatures of the boundary CFT.”
Comments on holographic entanglement entropy and RG flows (2012, background): “see [79, 80, 82], there is no general derivation of this holographic formula (3.”
Holographic calculations of Rényi entropy (2011, background): “It is well known that, for any even d, the universal contribution to the entanglement entropy of a CFT has a logarithmic dependence on the UV cut-off with a coefficient given by some linear combination of the central charges appearing in the trace anomaly [5, 21, 37, 8].”
Causal holographic information (2012, background): “If higher derivative curvature terms are present in the bulk then we need to consider a suitably generalized functional as has been discussed in [22, 23].”
Entanglement entropy from a holographic viewpoint (2012, background): “Even for them the understanding is currently limited, the holographic entanglement entropy has been found only for the Lovelock gravities [104, 105] (see also later developments [81, 106]).”
Distributional Geometry of Squashed Cones (2013, background): “19) has been suggested in [14] for surfaces with vanishing extrinsic curvatures and for a generic surfaces in the Gauss-Bonnet gravity in [16],[17].”
Holographic mutual information is monogamous (2011, background): “A general formula for the functional F has not been proposed, but formulas applying for certain types of corrections to the gravitational action have been proposed and tested in [23, 24].”
Relative entropy and holography (2013, neutral): “, see [17–19].”
Mutual information and the F-theorem (2015, background): “1) assumes that the bulk theory corresponds to Einstein gravity and this expression has been extended to certain higher curvature theories as well [88, 90] — see also [91–99].”
Quantum corrections to holographic entanglement entropy (2013, result): “However see [18–21] for R corrections.”
Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “Although this curvature-squared term does not effect the bulk equations of motion, it will contribute to the generalized entropy [101, 106]”
Some calculable contributions to holographic entanglement entropy (2011, methodology): “, see [4, 3, 6], there is no general derivation of this holographic formula (1.”
Entanglement entropy: Holography and renormalization group (2018, neutral): “(59) are rewritten in more concise forms (Hung et al., 2011b; Nakaguchi and Nishioka, 2016): S̃(β) ≥ 0 , E(β) ≥ 0 , C(β) ≥ 0 .”
Bit Threads and Holographic Entanglement (2016, methodology): “In the simplest gravity theories where the Einstein-Hilbert action is extended to higher-order terms in the curvature tensor, namely Gauss-Bonnet gravity, it is believed [27,28] that the area on the gravity side of the RT formula area should be replaced with ∫ d A(1 + αR) (and minimization should be”
Holographic entanglement entropy for general higher derivative gravity (2013, methodology): “rescription for the entanglement entropy in theories dual to higher derivative gravity. However, this cannot be correct because it would give wrong universal terms in the case of Gauss-Bonnet gravity [9]. On the other hand, there exists a dierent formula for the black hole entropy in Lovelock gravit”
Towards a derivation of holographic entanglement entropy (2011, background): “At the same time, we can add that for generic entangling surfaces, the bulk surface determining the holographic entanglement entropy will not play the role of the event horizon for some black hole [11, 41].”
Entanglement Entropy of Black Holes (2011, background): “On the other hand, in the absence of rotational symmetry i) there may appear terms in the entropy that are “missing” in the naively applied conical space approach: the extrinsic curvature contributions [204] or even some curvature terms [134].”
Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “If we abandon the strong coupling limit, we expect higher derivative corrections to the Einstein gravity and the holographic entanglement entropy also includes higher derivative terms [43, 44].”
Holographic c-theorems in arbitrary dimensions (2010, background): “There has also been some other recent progress in understanding holographic entanglement entropy with higher curvature theories in the bulk [ 65 , 121].”