February 6, 2024 | Herman Verlinde and Mengyang Zhang
This 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 charge adding up to $ c_{+} + c_{-} = 26 $. The authors show 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. They 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 $. The 2D Liouville-de Sitter gravity model is shown to arise from quantizing 3D de Sitter gravity. The paper establishes a precise quantitative correspondence between the doubled SYK model and the 2D Liouville-de Sitter gravity by matching the DSSYK two-point function with the boundary two-point function of the Liouville model. This result provides further evidence in support of an exact dual equivalence between these models. The paper is organized into sections that review the doubled SYK model, 3D de Sitter gravity, and the 2D Liouville-de Sitter gravity model, and discuss their properties and the correspondence between them. The authors conclude that the high temperature limit of the double scaled SYK model is a microscopic dual to low dimensional de Sitter gravity.This 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 charge adding up to $ c_{+} + c_{-} = 26 $. The authors show 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. They 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 $. The 2D Liouville-de Sitter gravity model is shown to arise from quantizing 3D de Sitter gravity. The paper establishes a precise quantitative correspondence between the doubled SYK model and the 2D Liouville-de Sitter gravity by matching the DSSYK two-point function with the boundary two-point function of the Liouville model. This result provides further evidence in support of an exact dual equivalence between these models. The paper is organized into sections that review the doubled SYK model, 3D de Sitter gravity, and the 2D Liouville-de Sitter gravity model, and discuss their properties and the correspondence between them. The authors conclude that the high temperature limit of the double scaled SYK model is a microscopic dual to low dimensional de Sitter gravity.