Double-scaled SYK and de Sitter holography

A bstract 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 $$ {\mathcal{O}}_{\Delta } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mtext>∆</mml:mtext> </mml:msub> </mml:math> 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∆(1 – ∆) in a 3D de Sitter space-time with radius R dS / G N = 4 πN / 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.