Holographic entanglement entropy conjecture for general spacetimes

Sanches, Fabio; Weinberg, Sean J.

doi:10.1103/physrevd.94.084034

Cited by 49 publications

(91 citation statements)

References 30 publications

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“…The first approach is to start with the RT or HRT proposal, and study the implications in the holographic dual, see [65][66][67][68][69]. The second approach is to directly propose a prescription in the bulk, and check its consistency [70,71]. The third approach, which we will advocated in the current paper, is to derive an analog of RT proposal using the dictionary of holography, along the lines of [60][61][62][63][64].…”

Section: Jhep07(2017)142mentioning

confidence: 99%

Entanglement entropy in flat holography

Jiang

Song

Wen

2017

J. High Energ. Phys.

122

301

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BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.

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Section: Jhep07(2017)142mentioning

confidence: 99%

Entanglement entropy in flat holography

Jiang

Song

Wen

2017

J. High Energ. Phys.

122

301

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“…Previous work has focused on generating them from null foliations (e.g. [7,8,12]), building the leaves of the holographic screen by finding a codimension-two surface with JHEP02(2018)049 Figure 1. A holographic screen can be constructed by null foliation from an observer's light cones.…”

Section: Jhep02(2018)049mentioning

confidence: 99%

Marginally trapped surfaces and AdS/CFT

Grado-White

Marolf

2018

J. High Energ. Phys.

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It has been proposed that the areas of marginally trapped or anti-trapped surfaces (also known as leaves of holographic screens) may encode some notion of entropy. To connect this to AdS/CFT, we study the case of marginally trapped surfaces anchored to an AdS boundary. We establish that such boundary-anchored leaves lie between the causal and extremal surfaces defined by the anchor and that they have area bounded below by that of the minimal extremal surface. This suggests that the area of any leaf represents a coarse-grained von Neumann entropy for the associated region of the dual CFT. We further demonstrate that the leading area-divergence of a boundary-anchored marginally trapped surface agrees with that for the associated extremal surface, though subleading divergences generally differ. Finally, we generalize an argument of Bousso and Engelhardt to show that holographic screens with all leaves anchored to the same boundary set have leaf-areas that increase monotonically along the screen, and we describe a construction through which this monotonicity can take the more standard form of requiring entropy to increase with boundary time. This construction is related to what one might call future causal holographic information, which in such cases also provides an upper bound on the area of the associated leaves.

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“…A construction analogous to holographic entanglement entropy, but which arises in generic realistic 7 spacetimes, was introduced in [8]. The basic idea of this approach is simple: in spacetimes with no conformal boundary, we consider instead a surface which has properties suggestive of holographic duality and which reduces to the conformal boundary in the appropriate cases.…”

Section: A Holography In General Spacetimes and New Dynamical Inequamentioning

confidence: 99%

“…Holographic screens [13], and especially their special case of past and future holographic screens [12,14], are ideal surfaces for these purposes. 8 The screen entanglement proposal [8] is the postulate that minimal extremal surfaces anchored to the unique time slices of past or future holographic screens are in fact von Neumann entropies for a quantum state despite the fact that no framework is known for the quantum mechanics of completely general spacetimes. This proposal is falsifiable even without such a framework as we now explain.…”

Section: A Holography In General Spacetimes and New Dynamical Inequamentioning

confidence: 99%

“…While they are generally regarded as restrictions on the class of states that are suitable to have holographically dual spacetimes, we suggest here that they may also play an additional role: guaranteeing that holographic entanglement entropy is consistent with quantum mechanics. This idea can be used to explore the possibility that covariant holographic entanglement entropy can be extended beyond the scope of the AdS/CFT correspondence [8]. In particular, if the inequalities of holographic entanglement entropy are strong enough, then extremal surface constructions in general realistic spacetimes must be consistent with quantum mechanics as explained in Sec.…”

Section: Introductionmentioning

confidence: 99%

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New constraints for holographic entropy from maximin: A no-go theorem

Rota

Weinberg

2018

Phys. Rev. D

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The Ryu-Takayanagi (RT) formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the Rangamani-Hubeny-Takayanagi (HRT) formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for five regions. This inequality, while not maximin provable, is much weaker than many of the inequalities satisfied by the RT formula and should therefore be easier to prove. If it is valid, then there is strong evidence that holographic entanglement entropy plays a role in general spacetimes including those that arise in cosmology. Our new inequality is obtained by the assumption that the HRT formula satisfies every known balanced inequality obeyed by the Shannon entropies of classical probability distributions. This is a property that the RT formula has been shown to possess and which has been previously conjectured to hold for quantum mechanics in general.

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Holographic entanglement entropy conjecture for general spacetimes

Cited by 49 publications

References 30 publications

Entanglement entropy in flat holography

Entanglement entropy in flat holography

Marginally trapped surfaces and AdS/CFT

New constraints for holographic entropy from maximin: A no-go theorem

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