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Holographic Entanglement Entropy in the dS/CFT Correspondence and Entanglement Entropy in the Sp(N) Model

Yoshiki Sato

Published Mar 23, 2016• 0 citations
Publisher
DOI
10.14989/doctor.k19494

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We show that the quantum entanglement between the conformal field theories (CFTs) living on the future and past boundaries in the de Sitter/conformal field theory (dS/CFT) correspondence can be described by Wick rotating to a geometry with two timelike directions. We propose a new realization of the dS/CFT correspondence in which quantum gravity on this two-time geometry is holographically dual to a CFT defined on a Lorentzian torus. We show that this duality reproduces key features of dS holography, including the dS entropy, correlation functions, and pseudoentropy. Finally, by extending the framework of path-integral optimization, we explain how dS spacetime emerges from the CFT on the Lorentzian torus.
In recent years, the holographic duality between T T ¯ -deformed conformal field theory (CFT) and Anti-de Sitter (AdS) spacetime with finite radial cutoff has received significant attention. The study of T T ¯ deformation within the framework of de Sitter (dS)/CFT duality has also progressed. This paper shows that the trace flow equation in dS spacetime can be analytically extended from its AdS counterpart through double Wick rotations. Meanwhile, we generalize the replica method in both AdS and dS holography to derive a general expression for the entanglement entropy of arbitrary single spatial intervals within the T T ¯ -deformed framework. For both finite size and finite temperature systems, we obtain the analytical expression for the entanglement entropy after T T ¯ deformation. Finally, in dS/dS holography and half-dS holography, we find that the dual field theory exhibits nonlocality by analyzing the strong subadditivity and boosted strong subadditivity of entanglement entropy.
We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.