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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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De Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes
The Goheer–Kleban–Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests that the classical symmetry between different static patches is broken and that eternal de Sitter space—if it exists at all—is an ensemble average.
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- Award ID(s):
- 2014215
- PAR ID:
- 10285031
- Date Published:
- Journal Name:
- Universe
- Volume:
- 7
- Issue:
- 12
- ISSN:
- 2218-1997
- Page Range / eLocation ID:
- 464
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A<sc>bstract</sc> We propose a new model of low dimensional de Sitter holography in the form of a pair of double-scaled SYK models at infinite temperature coupled via an equal energy constraintHL=HR. As a test of the duality, we compute the two-point function between two dressed SYK operators$$ {\mathcal{O}}_{\Delta } $$ that preserve the constraint. We find that in the largeNlimit, the two-point function precisely matches with the Green’s function of a massive scalar field of mass squaredm2= 4∆(1 – ∆) in a 3D de Sitter space-time with radiusRdS/GN= 4πN/p2. In this correspondence, the SYK time is identified with the proper time difference between the two operators. We introduce a candidate gravity dual of the doubled SYK model given by a JT/de Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter gravity. We comment on the physical meaning of the finite de Sitter temperature and entropy.more » « less
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A<sc>bstract</sc> We study the partition function of 3D de Sitter gravity defined as the trace over the Hilbert space obtained by quantizing the phase space of non-rotating Schwarzschild-de Sitter spacetime. Motivated by the correspondence with double scaled SYK, we identify the Hamiltonian with the gravitational Wilson-line that measures the conical deficit angle. We express the Hamiltonian in terms of canonical variables and find that it leads to the exact same chord rules and energy spectrum as the double scaled SYK model. We use the obtained match to compute the partition function and scalar two-point function in 3D de Sitter gravity.more » « less
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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.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/universe7120464
