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1. Out-of-time-order correlators and Lyapunov exponents in sparse SYK

   Caceres, Elena; Guglielmo, Tyler; Kent, Brian; Misobuchi, Anderson (November 2023, The journal of high energy physics)

   We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N, the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq)n. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N. 

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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 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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4. Spectral form factor in sparse SYK models

   https://doi.org/10.1007/JHEP08(2022)236  

   Cáceres, Elena; Misobuchi, Anderson; Raz, Amir (August 2022, Journal of High Energy Physics)

   A<sc>bstract</sc> We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value ofNout of reach of current numerical simulations. 

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5. SYK correlators from 2D Liouville-de Sitter gravity

   https://doi.org/10.1007/JHEP05(2025)053  

   Verlinde, Herman; Zhang, Mengyang (May 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We introduce and study a candidate gravity dual to the double scaled SYK model in the form of an exactly soluble 2D de Sitter gravity model consisting of two spacelike Liouville CFTs with complex central charge adding up toc₊+c₋= 26. In [1] it was shown that the two-point function of physical operators in a doubled SYK model matches in the semi-classical limit with the Green’s function of a massive scalar field in 3D de Sitter space. As further evidence of the duality, we adapt a result from Zamolodchikov to compute the boundary two-point function of the 2D Liouville-de Sitter gravity model on a disk and find that it reproduces the exact DSSYK two-point function to all orders inλ=p²/N. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity. 

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