Double-scaled SYK and de Sitter holography

Abstract

We propose a new model of low dimensional de Sitter holography in the form of a pair of double-scaled SYK models at infinite temperature coupled via an equal energy constraint H_L = H_R. As a test of the duality, we compute the two-point function between two dressed SYK operators \( {\mathcal{O}}_{\Delta } \) that preserve the constraint. We find that in the large N limit, the two-point function precisely matches with the Green’s function of a massive scalar field of mass squared m² = 4∆(1 – ∆) in a 3D de Sitter space-time with radius R_dS/G_N = 4πN/p². In this correspondence, the SYK time is identified with the proper time difference between the two operators. We introduce a candidate gravity dual of the doubled SYK model given by a JT/de Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter gravity. We comment on the physical meaning of the finite de Sitter temperature and entropy.