De Sitter Holography and Entanglement Entropy
Apr 23, 2018
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Abstract: (Springer)
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.Note:
- 23 pages, 4 figures; v2: new references and acknowledgement added
- Gauge-gravity correspondence
- AdS-CFT Correspondence
- Conformal Field Theory
- Black Holes
- field theory: conformal
- entropy: entanglement
- horizon: entropy
- gravitation: constraint
- dimension: 1
- de Sitter
References(66)
Figures(3)