Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model

TL;DR

This paper explores the pole-skipping phenomenon in two-dimensional de Sitter spacetime and establishes a numerical correspondence with the double-scaled SYK model at infinite temperature, linking quantum gravity and quantum many-body systems.

Contribution

It develops the pole-skipping structure in 2D de Sitter space and connects it with the double-scaled SYK model, providing a concrete realization of the DS/dS correspondence.

Findings

Pole-skipping points satisfy specific frequency relations in dS spacetime.

A one-to-one correspondence between dS pole-skipping points and DSSYK$_ finite$ model in the classical limit.

Numerical evidence linking quantum gravity in dS to a quantum many-body system.

Abstract

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation $\omega_{dS}=i2\pi T_{dS}(1-s)$, where $T_{dS}=1/2\pi L$ and $s$ denotes spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon $r=L$ for the scalar field of spin-0 and the fermionic field of spin-$\frac{1}{2}$ correspond one-to-one with those in the classical limit as $\lambda\rightarrow 0$ in double-scaled Sachdev-Ye-Kitaev model when the temperature is infinite (DSSYK$_\infty$). This provides a numerical correspondence between quantum gravity in the static patch of two-dimensional dS spacetime and a one-dimensional quantum system, which we consider as a realization of the DS/dS correspondence.