Some Information Theoretic Aspects of De-Sitter Holography

Abstract

Built on our observation that entangling surfaces of the boundary field theory are great co-dimension one spheres in the context of DS/dS correspondence, we study some information theoretic quantities of the field theory dual intensively using holographic proposals. We will focus on entanglement entropy (EE), entanglement of purification (EoP) and complexity. Several fundamental observations and analysis are provided. For EE, we focus on its scaling behavior, which indicates the nature of the relevant degrees of freedom. Moreover, we find that EE provides us with important information of the energy spectrum in pure dS and it also leads us to the speculation that the field theory dual is chaotic or non-integrable. For EoP, an interesting phenomenon we call "Entanglement of Purification Jump" is observed according to which we propose two puzzles regarding EoP and EE in the context of dS holography. For complexity, we find that the Complexity=Volume proposal does not provide a well-defined way to compute complexity for pure dS. However, it does provide a well-defined way to compute complexity in the $T\bar{T}+{\Lambda }_2$ deformed case. At the end, we will use the surface/state correspondence to resolve all the puzzles and hence reach a consistent information theoretic picture of dS holography. Moreover, we will provide evidence for our former proposal that the $T\bar{T}+\cdots$ deformations are operating quantum circuits and study the non-locality of the field theory algebra suggested by the surface/state correspondence.

26 pages,13 figures, references added

References in corpus (2)

• Surface/State Correspondence as a Generalized Holography
• Entropy, Entanglement and Swampland Bounds in DS/dS

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• Modular Hamiltonian for de Sitter diamonds
• Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model
• Relative Entropy in de Sitter is a Noether Charge
• Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• Analog de Sitter universe in quantum Hall systems with an expanding edge
• Entropy-area law and temperature of de Sitter horizons from modular theory
• Soft thermodynamics of gravitational shock wave
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
• Holographic CCFT Pseudo-Entropy
• Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff