De Sitter holography and entanglement entropy

• Main Authors: Xi Dong, Eva Silverstein, Gonzalo Torroba
• Format: Article
• Language: English
• Published: SpringerOpen 2018-07-01
• Series: Journal of High Energy Physics
• Subjects: Gauge-gravity correspondence; AdS-CFT Correspondence; Conformal Field Theory; Black Holes
• Online Access: http://link.springer.com/article/10.1007/JHEP07(2018)050

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.