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De Sitter holography and entanglement entropy

  • Xi DongEmail author
  • Eva Silverstein
  • Gonzalo Torroba
Open Access
Regular Article - Theoretical Physics

Abstract

We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d + 1 dimensions involves two coupled CFT sectors constrained by residual d-dimensional gravity. In the d = 2 case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large central charge and a sparse light spectrum, derived by Hartman, Keller, and Stoica. Significant interactions between the two CFTs, derived previously for other reasons, suggest a maximally mixed state upon tracing out one of the two sectors; we derive this by determining the holographic Renyi entropies. The resulting entanglement entropy matches the Gibbons-Hawking formula for de Sitter entropy, including the numerical coefficient. Finally, we interpret the Gibbons-Hawking horizon entropy in terms of the Ryu-Takayanagi entropy, and explore the time evolution of the entanglement entropy.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence Conformal Field Theory Black Holes 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  3. 3.Centro Atómico Bariloche and CONICETBarilocheArgentina

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