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It has been argued that the entanglement spectrum of a static patch of de Sitter space must be flat, or what is equivalent, the temperature parameter in the Boltzmann distribution must be infinite. This seems absurd: quantum fields in de Sitter space have thermal behavior with a finite temperature proportional to the inverse radius of the horizon. The resolution of this puzzle is that the behavior of some quantum systems can be characterized by a temperature-like quantity which remains finite as the temperature goes to infinity. For want of a better term we have called this quantity tomperature. In this paper we will explain how tomperature resolves the puzzle in a proposed toy model of de Sitter holography -- the double-scaled limit of SYK theory.
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Entanglement and Chaos in De Sitter Space Holography: An SYK Example
Entanglement, chaos, and complexity are as important for de Sitter space as for AdS, and for black holes. There are similarities and also great differences between AdS and dS in how these concepts are manifested in the space-time geometry.In the first part of this paper the Ryu–Takayanagi prescription, the theory of fast-scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be ``hyperfast."In the later part of the paper I show that a certain limit of the SYK model satisfies the hyperfast criterion. This leads tothe radical conjecture that a limit of SYK is indeed a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.
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- Award ID(s):
- 2014215
- PAR ID:
- 10352546
- Date Published:
- Journal Name:
- Journal of holography applications in physics
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2783-3518
- Page Range / eLocation ID:
- 1-22
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.22128/JHAP.2021.455.1005
