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 ${\cal O}_\Delta$ 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 $m^2 = 4\Delta(1-\Delta)$ in a 3D de Sitter space-time with radius $R_{\text{dS}}/G_N = 4\pi N/p^2$. 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.