SYK Correlators from 2D Liouville-de Sitter Gravity

TL;DR

This paper proposes a 2D de Sitter gravity model with Liouville CFTs as a dual to the double scaled SYK model, matching boundary correlators and deriving from 3D de Sitter gravity quantization.

Contribution

It introduces an exactly solvable 2D de Sitter gravity model with Liouville CFTs as a dual to the double scaled SYK model, providing exact correlator matches.

Findings

Boundary two-point functions match the DSSYK model to all orders in λ.

The 2D Liouville-de Sitter model is derived from quantizing 3D de Sitter gravity.

The model offers a new exactly solvable holographic dual for SYK-like systems.

Abstract

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 $\lambda=p^2/N$. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity.