Flat entanglement spectra in fixed-area states of quantum gravity
A bstract We use the Einstein-Hilbert gravitational path integral to investigate gravita- tional entanglement at leading order O (1 /G ). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hub...
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Published in | The journal of high energy physics Vol. 2019; no. 10; pp. 1 - 25 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2019
Springer Nature B.V Springer Berlin SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | A
bstract
We use the Einstein-Hilbert gravitational path integral to investigate gravita- tional entanglement at leading order
O
(1
/G
). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies
Sn
are independent of
n
at this order. The
n
-dependence of
Sn
in more general states then arises from sums over the RT/HRT- area, which are generally dominated by different values of this area for each
n
. This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of alge- braic centers which arise in the quantum error-correcting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh. |
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Bibliography: | SC0018944; SC0019127 USDOE Office of Science (SC) |
ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP10(2019)240 |