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1. Double-scaled SYK and de Sitter holography

   https://doi.org/10.1007/JHEP05(2025)032  

   Narovlansky, Vladimir; Verlinde, Herman (May 2025, Journal of High Energy Physics)

   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 constraintH_L=H_R. As a test of the duality, we compute the two-point function between two dressed SYK operators$$ {\mathcal{O}}_{\Delta } $$ $O_{\text{∆}}$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 radiusR_dS/G_N= 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. 

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2. Large p SYK from chord diagrams

   https://doi.org/10.1007/JHEP09(2023)154  

   Mukhametzhanov, Baur (September 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: “large p” SYK 1 ≪p≪Nand “double-scaled” SYKN,p → ∞withλ= 2p²/Nfixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean 2n-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the$$ {\mathcal{U}}_q\left( su\left(1,1\right)\right) $$ $U_q\left(\mathrm{su}\left(1,1\right)\right)$6j-symbol. 

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3. Double-scaled SYK, chords and de Sitter gravity

   https://doi.org/10.1007/JHEP03(2025)076  

   Verlinde, Herman (March 2025, Journal of High Energy Physics)

   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. 

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4. Complexity and momentum

   https://doi.org/10.1007/JHEP03(2021)239  

   Susskind, Leonard; Zhao, Ying (March 2021, Journal of High Energy Physics)

   A bstract Previous work has explored the connections between three concepts — operator size, complexity, and the bulk radial momentum of an infalling object — in the context of JT gravity and the SYK model. In this paper we investigate the higher dimensional generalizations of these connections. We use a toy model to study the growth of an operator when perturbing the vacuum of a CFT. From circuit analysis we relate the operator growth to the rate of increase of complexity and check it by complexity-volume duality. We further give an empirical formula relating complexity and the bulk radial momentum that works from the time that the perturbation just comes in from the cutoff boundary, to after the scrambling time. 

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5. Replica wormholes and the black hole interior

   https://doi.org/10.1007/JHEP03(2022)205  

   Penington, Geoff; Shenker, Stephen H.; Stanford, Douglas; Yang, Zhenbin (March 2022, Journal of High Energy Physics)

   A<sc>bstract</sc> Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description. 

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