Complex entangling surfaces for AdS and Lifshitz black holes?

We discuss the possible relevance of complex codimension-two extremal surfaces to the Ryu-Takayanagi holographic entanglement proposal and its covariant Hubeny-Rangamani-Takayanagi generalization. Such surfaces live in a complexified bulk spacetime defined by analytic continuation. We identify surfa...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 31; no. 21; pp. 1 - 29
Main Authors Fischetti, Sebastian, Marolf, Donald
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.11.2014
Subjects
AdS/CFT
black holes
Black holes (astronomy)
conformal field theory
Control surfaces
Entanglement
entanglement entropy
Entropy
Mathematical analysis
Proposals
Quantum gravity
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Summary:We discuss the possible relevance of complex codimension-two extremal surfaces to the Ryu-Takayanagi holographic entanglement proposal and its covariant Hubeny-Rangamani-Takayanagi generalization. Such surfaces live in a complexified bulk spacetime defined by analytic continuation. We identify surfaces of this type for BTZ, Schwarzschild-AdS, and Schwarzschild-Lifshitz planar black holes. Since the dual CFT interpretation for the imaginary part of their areas is unclear, we focus on a straw man proposal relating CFT entropy to the real part of the area alone. For Schwarzschild-AdS and Schwarzschild-Lifshitz, we identify families where the real part of the area agrees with qualitative physical expectations for the time-dependence of the appropriate CFT entropy and, in addition, where it is smaller than the area of corresponding real extremal surfaces. It is thus plausible that the CFT entropy is controlled by these complex extremal surfaces.
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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/31/21/214005