Double-scaled SYK, Chords and de Sitter Gravity

TL;DR

This paper connects 3D de Sitter gravity with double scaled SYK, showing they share the same energy spectrum and chord rules, and uses this to compute key physical quantities.

Contribution

It identifies the Hamiltonian of 3D de Sitter gravity with a gravitational Wilson-line, matching the double scaled SYK model's spectrum and rules.

Findings

Hamiltonian matches double scaled SYK spectrum

Partition function computed using the SYK correspondence

Scalar two-point function derived in de Sitter gravity

Abstract

We study the partition function of 3D de Sitter gravity defined as the trace over the Hilbert space obtained by quantizing the phase space of non-rotating Schwarzschild-de Sitter spacetime. Motivated by the correspondence with double scaled SYK, we identify the Hamiltonian with the gravitational Wilson-line that measures the conical deficit angle. We express the Hamiltonian in terms of canonical variables and find that it leads to the exact same chord rules and energy spectrum as the double scaled SYK model. We use the obtained match to compute the partition function and scalar two-point function in 3D de Sitter gravity.