Locality of Gravitational Systems from Entanglement of Conformal Field Theories

Lin, Jennifer; Marcolli, Matilde; Ooguri, Hirosi; Stoica, Bogdan

doi:10.1103/physrevlett.114.221601

Cited by 83 publications

(109 citation statements)

References 23 publications

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“…We recognize that (14) are exactly the conditions on conformal boundary states located at the equator of the Euclidean S d related to the the t = 0 slice of the Lorentzian R × S d−1 by the Wick rotation t = −iτ . They preserve More generally, when the bulk local operatorψ carries a non-trivial spin, |ψ…”

Section: Jhep10(2015)114mentioning

confidence: 65%

“…Existence of these states suggests that conformal boundary conditions (14) can be generalized so that boundary states are not invariant under the SO(1, d) subgroup of the conformal symmetry but are in its finite dimensional representation. It would be interesting to explore their interpretation from the point of view of CFT.…”

Section: Jhep10(2015)114mentioning

confidence: 99%

“…The use of boundary states in constructing bulk local operators may be related to the computation of the bulk energy density by the Radon transform of the entanglement entropy in [14] and to the integral geometry discussed in [15]. We would also like to find out to what extent our proposal depends on the AdS background.…”

Section: Jhep10(2015)114mentioning

confidence: 99%

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Bulk locality and boundary creating operators

Nakayama

Ooguri

2015

J. High Energ. Phys.

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139

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We formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary dilatation obey free field equations in AdS and that incorporating bulk interactions require their superpositions. We also comment on the recent proposals by Kabat et al., and by H. Verlinde.

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Section: Jhep10(2015)114mentioning

confidence: 65%

Section: Jhep10(2015)114mentioning

confidence: 99%

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Bulk locality and boundary creating operators

Nakayama

Ooguri

2015

J. High Energ. Phys.

Self Cite

139

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“…Notably, when the formula is applied to the case of the two-sided black hole geometry, one finds that the Einstein-Rosen bridge encodes entanglement of thermofield double degrees of freedom in the boundary CFT [6,7]. Moreover, the Ryu-Takayanagi formula has been used to derive the linearized Einstein equations in AdS [2,8], as well as to obtain integrated energy conditions [9,10]. These examples all demonstrate important connections between bulk geometry and entanglement data on the boundary.…”

Section: Jhep09(2015)130mentioning

confidence: 99%

The holographic entropy cone

Bao

Nezami

Ooguri

et al. 2015

J. High Energ. Phys.

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173

510

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We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

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“…In quantum information there are several quantities which could provide measures to compare two states. These include, for example, relative entropy or fidelity (see [16] for a holographic description of the relative entropy). The aim of this section is to investigate whether there is any connection between holographic complexity and fidelity.…”

Section: Fidelity and Holographic Complexitymentioning

confidence: 99%

Holographic complexity

2015

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For a field theory with a gravitational dual, following Susskind's proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a codimension one time slice in the bulk geometry enclosed by the extremal co-dimension two hypersurface appearing in the computation of the holographic entanglement entropy. The proportionally constant, up to a numerical order of one factor is GR where G is the Newton constant and R is the curvature of the space time. We study this quantity in certain holographic models. We also explore a possible relation between the defined quantity and fidelity appearing in quantum information literature.

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Locality of Gravitational Systems from Entanglement of Conformal Field Theories

Cited by 83 publications

References 23 publications

Bulk locality and boundary creating operators

Bulk locality and boundary creating operators

The holographic entropy cone

Holographic complexity

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