Bootstrapping quantum extremal surfaces. Part I. The area operator

Belin, Alexandre; Colin-Ellerin, Sean

doi:10.1007/jhep11(2021)021

Cited by 19 publications

(27 citation statements)

References 62 publications

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“…Indeed minimally coupled scalar scalars in AdS 3 are to dual generalised free fields [16]. As shown recently, these correlation functions get corrected at order O(1/c) [26]. Here, we will restrict our attention to the leading order in c. The connected part of the four point function in (4.2) is given by…”

Section: Generalised Free Fieldsmentioning

confidence: 90%

“…For global descendants of generalised free fields and descendants of the vacuum the modification to the leading contributions to the single interval entanglement entropy are universal and are given by (4.6), (4.19). It should be possible to verify these results by generalizing the methods of [16,25,26] in the bulk. This would show how the Ryu-Takanayagi surface as well as bulk entanglement entropy across this surface are modified by the action of the isometries.…”

Section: Jhep02(2022)003 5 Conclusionmentioning

confidence: 97%

“…Entanglement entropy of descendants of the vacuum are universal to all conformal field theories and in particular for holographic conformal field theories. It should be possible to use the methods developed in [16,25,26] to verify the results of this section.…”

Section: Applicationsmentioning

confidence: 99%

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Entanglement in descendants

Chowdhury

David

2022

J. High Energ. Phys.

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We study the single interval entanglement and relative entropies of conformal descendants in 2d CFT. Descendants contain non-trivial entanglement, though the entanglement entropy of the canonical primary in the free boson CFT contains no additional entanglement compared to the vacuum, we show that the entanglement entropy of the state created by its level one descendant is non-trivial and is identical to that of the U(1) current in this theory. We determine the first sub-leading corrections to the short interval expansion of the entanglement entropy of descendants in a general CFT from their four point function on the n-sheeted plane. We show that these corrections are determined by multiplying squares of appropriate dressing factors to the corresponding corrections of the primary. Relative entropy between descendants of the same primary is proportional to the square of the difference of their dressing factors. We apply our results to a class of descendants of generalized free fields and descendants of the vacuum and show that their dressing factors are universal.

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Section: Generalised Free Fieldsmentioning

confidence: 90%

Section: Jhep02(2022)003 5 Conclusionmentioning

confidence: 97%

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Entanglement in descendants

Chowdhury

David

2022

J. High Energ. Phys.

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“…The QES proposal hasn't been proven, however it is believed to be correct since it satisfies some non trivial consistency checks which we will review in section 2.2. This proposal has been checked order by order in for a few sub-leading corrections by comparing computations in the bulk with those in the dual boundary CFT [73][74][75].…”

Section: Partial Proof Of the Quantum Extremal Surface Proposalmentioning

confidence: 99%

“…This therefore proves that the holographic entanglement entropy proposal agrees with the RT/HRT and FLM formulas at the appropriate orders. The FLM formula and the QES proposal will not agree at higher orders in and one can perform computations at higher orders to determine if the QES proposal is correct [73][74][75]. The QES proposal passes some essential consistency checks and is therefore believed to be correct.…”

Section: Gmentioning

confidence: 99%

Holographic spacetime, black holes and quantum error correcting codes: A review

Kibe,

Mandayam,

Mukhopadhyay

2021

Preprint

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This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

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Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation

Chen

Wang

2023

J. High Energ. Phys.

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Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the entanglement wedge reconstruction in the context of subregion duality in AdS/CFT. In this paper, we study the perturbation theory of the causal shadows and their relation to the properties of the associated modular flows. We first revisit the cases of degenerate causal shadows based on known examples, and discuss the origin for their degeneracy via the local nature of the modular flow. We then focus on the perturbative case in which the CFT subregion consists of two spheres separated by a large distance L ≫ R1,2. The RT surfaces still agree with the causal horizons, giving a degenerate causal shadow classically. We compute the corrections to the quantum extremal surfaces (Q.E.S) from the bulk mutual information, which then give rise to a non-degenerate causal shadow at order GN. We end by discussing the causal shadow perturbation theory more generally, in particular we explore the possibility of extracting the positivity conditions characterizing perturbative causal shadows in the boundary CFTs.

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Bootstrapping quantum extremal surfaces. Part I. The area operator

Cited by 19 publications

References 62 publications

Entanglement in descendants

Entanglement in descendants

Holographic spacetime, black holes and quantum error correcting codes: A review

Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation

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