Extracting spacetimes using the AdS/CFT conjecture

Bilson, Samuel

doi:10.1088/1126-6708/2008/08/073

Cited by 36 publications

(51 citation statements)

References 21 publications

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“…11 Ref. [20] showed that AdS-Schwarzschild black holes are similar in this respect to BTZ black holes: they have 11 We thank Mukund Rangamani and Mark Van Raamsdonk for clarifying this issue and for pointing out refs. [68,69].…”

Section: Toward Higher Dimensionsmentioning

confidence: 99%

“…Recently, we proposed a new quantity, the differential entropy, constructed out of entanglement, that reconstructs the areas of closed surfaces in AdS that do not asymptote to the boundary [4][5][6][7][8]. 2 By shrinking such closed surfaces one can attempt to reconstruct local geometry in AdS space from purely field theoretic objects [10][11][12][13][14]. The relevance of boundary entanglement for such a reconstruction was first pointed out in [9,[15][16][17], see also [18].…”

Section: Introductionmentioning

confidence: 99%

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Entwinement and the emergence of spacetime

Balasubramanian

Chowdhury

Czech

et al. 2015

J. High Energ. Phys.

156

279

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It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -a 2d conformal field theory (CFT) that is dual to a conical defect in AdS 3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.

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Section: Toward Higher Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entwinement and the emergence of spacetime

Balasubramanian

Chowdhury

Czech

et al. 2015

J. High Energ. Phys.

156

279

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show abstract

“…Refs. [56][57][58] gave another algorithm for recovering non-trivial components of the metric in symmetric setups from analytic properties of field theory quantities, including entanglement entropies. The results of the present appendix are complementary to that development: they highlight the information-theoretic structure underlying the organization of the bulk and can accommodate less symmetric inputs.…”

Section: B Point-curves and Bulk Reconstructionmentioning

confidence: 99%

Integral geometry and holography

Czech

Lamprou

McCandlish

et al. 2015

J. High Energ. Phys.

196

438

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We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS 3 /CFT 2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the RyuTakayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -points, distances and angles -are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS 3 whose kinematic space is two-dimensional de Sitter space.

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“…1 Our ab initio construction of points and distances should be distinguished from [35][36][37][38], who use entanglement entropies or minimal surfaces to reconstruct numerically a metric assuming a certain ansatz. Equations (5)-(6) can be inverted [30,31].…”

Section: A Bulk Curvesmentioning

confidence: 99%

Holographic definition of points and distances

2014

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We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS 3 ). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS 3 corresponds to a collection of boundary intervals which is selected by a variational principle we discuss. Coordinates in AdS 3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS 3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS 3 -the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of nonminimal geodesics.

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Extracting spacetimes using the AdS/CFT conjecture

Cited by 36 publications

References 21 publications

Entwinement and the emergence of spacetime

Entwinement and the emergence of spacetime

Integral geometry and holography

Holographic definition of points and distances

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