Towards a full solution of the large N double-scaled SYK model

Abstract

We compute the exact, all energy scale, 4-point function of the large $N$ double-scaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of SL$(2)$, that generalizes the Schwarzian to the complete range of energies.

arXiv comment52+28 pages, 14 figures; v2: references revised, typos corrected, changed normalization of SL(2)_q 6j symbol

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• Quantum group origins of edge states in double-scaled SYK
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• Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model
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• Quantum Annealing with chaotic driver Hamiltonians
• Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
• Discrete Bulk Reconstruction
• Global density-dependent $\alpha$-nucleon interaction for $\alpha$-nucleus elastic scattering
• The quantum $p$-spin glass model: A user manual for holographers
• Detecting quantum chaos via pseudo-entropy
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• Fiducial observers and the thermal atmosphere in the black hole quantum throat
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• Cap amplitudes in random matrix models