SYK Correlators from 2D Liouville-de Sitter Gravity

SYK Correlators from 2D Liouville-de Sitter Gravity

February 6, 2024 | Herman Verlinde and Mengyang Zhang
The paper introduces and studies 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 charges adding up to \(c_+ + c_- = 26\). The authors 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 in \(\lambda = p^2/N\). They describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity. The paper is organized into several sections, covering the properties of the double scaled SYK model, 3D de Sitter gravity, and the 2D Liouville-de Sitter gravity model. The authors provide a detailed derivation of the 3D de Sitter gravity action and its quantization, leading to the identification of the wave functions with chiral Virasoro CFT partition functions. They then introduce the 2D Liouville-de Sitter gravity model and compute the boundary two-point function, which matches the exact DSSYK two-point function. This match provides strong evidence for the holographic duality between the double scaled SYK model and 2D Liouville-de Sitter gravity.The paper introduces and studies 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 charges adding up to \(c_+ + c_- = 26\). The authors 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 in \(\lambda = p^2/N\). They describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity. The paper is organized into several sections, covering the properties of the double scaled SYK model, 3D de Sitter gravity, and the 2D Liouville-de Sitter gravity model. The authors provide a detailed derivation of the 3D de Sitter gravity action and its quantization, leading to the identification of the wave functions with chiral Virasoro CFT partition functions. They then introduce the 2D Liouville-de Sitter gravity model and compute the boundary two-point function, which matches the exact DSSYK two-point function. This match provides strong evidence for the holographic duality between the double scaled SYK model and 2D Liouville-de Sitter gravity.
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