SYK Correlators from 2D Liouville-de Sitter Gravity

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 to $c_{+}+c_{-}=26$. 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 in $\lambda =p^2\mathrm{/}N$. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity.