De Sitter holography and entanglement entropy

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.

A preprint version of the article is available at ArXiv.

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Dong, X., Silverstein, E. & Torroba, G. De Sitter holography and entanglement entropy. J. High Energ. Phys. 2018, 50 (2018). https://doi.org/10.1007/JHEP07(2018)050

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Keywords

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