Generalized Free Fields in de Sitter from 1D CFT

TL;DR

This paper demonstrates that pairs of large N 1D CFTs contain a natural generalized free field algebra on a de Sitter geodesic, with implications for holography and the de Sitter/DSSYK correspondence.

Contribution

It constructs a generalized free field algebra within 1D CFT pairs using large N factorization and conformal symmetry, extending holographic maps to de Sitter space.

Findings

Identifies a natural sub-algebra of operators forming a generalized free field in 1D CFT pairs.

Extends the holographic map into the bulk of 3D de Sitter space, aligning with the HKLL prescription.

Connects the construction to covariant Schwarzian quantum mechanics and the de Sitter/DSSYK correspondence.

Abstract

We show that a pair of identical large $N$ 1D CFTs, like the low-energy limit of the SYK model or a line-defect inside a higher dimensional CFT, contains a natural sub-algebra of operators that comprise a generalized free field algebra living on a time-like geodesic in d+1-dimensional de Sitter spacetime. The construction uses large $N$ factorization, 1D conformal symmetry, and the split representation of de Sitter Green functions. We show that for 3D de Sitter spacetime, the holographic map extends into the bulk and reduces to the standard HKLL prescription adjusted to de Sitter spacetime. We describe how our construction is automatically implemented in a covariant version of Schwarzian quantum mechanics and comment on the relevance of our results to the de Sitter/DSSYK correspondence.