Deriving covariant holographic entanglement

Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund

doi:10.1007/JHEP11(2016)028

Title: Deriving covariant holographic entanglement

Journal Article · Mon Nov 07 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP11(2016)028· OSTI ID:1597743

Dong, Xi ^[1]; Lewkowycz, Aitor ^[2]; Rangamani, Mukund ^[3]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Princeton Univ., NJ (United States)
Univ. of California, Davis, CA (United States)

We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: SC0009988; PHYS-106629; PHY11-25915; PHY-1314198; PHY-1316699

OSTI ID:: 1597743

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 11; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 97 works

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