dS JT Gravity and Double-Scaled SYK

TL;DR

The paper investigates a proposed duality between the high-temperature double-scaled SYK model, $\mathrm{DSSYK}_{\infty}$, and a bulk theory given by two-dimensional JT gravity with positive cosmological constant (dS-JT). It identifies a bulk solution, dS$_2{}'$, as the dimensional reduction of $dS_3$ and analyzes its thermodynamics, entropy, and symmetry properties, establishing a framework for static patch holography. By computing one-sided bulk correlators and examining quasinormal modes, the work demonstrates how boundary correlators encode bulk physics, including a late-time exponential decay governed by tomperature $\mathcal{T}$ and a universal emergence timescale $t_* \sim \beta_{\mathrm{GH}}\log S$, with early-time bulk features linking boundary and horizon dynamics. The paper also outlines future directions, such as charged DSSYK, spacelike observables, and finite-$\lambda$ generalizations, to further probe and test the boundary-to-bulk dictionary and the role of bulk propagating fields.

Abstract

This paper pushes forward a conjecture made in [1] that a high-temperature double-scaled limit of the SYK model ($\mathrm{DSSYK}_{\infty}$) describes a de Sitter-like space. We identify a specific bulk theory which we conjecture to be dual to $\mathrm{DSSYK}_{\infty}$, namely JT gravity with positive cosmological constant (dS-JT). We focus our attention on a specific solution of dS-JT in which spacetime is a particular bounded submanifold of dS$_2$ and the profile of the dilaton coincides with that of the radial coordinate of a static patch. This solution can be understood as a dimensional reduction of dS$_3$ and was previously studied by [2] in a context different than ours. We describe the geometry of this solution in detail and discuss some ways in which the physics of this solution matches known physics of $\mathrm{DSSYK}_{\infty}$. We describe an example of holographic bulk emergence and find a new role for the timescale $t_* \sim β_{\mathrm{GH}}\log(S)$ as the timescale governing this emergence. We discuss some constraints on the boundary-to-bulk operator mapping. This paper provides additional background and context for a companion paper [3] by L. Susskind, which will appear simultaneously.

Figures (11)

• Figure 1: The pode stretched horizon (green) and the mathematical horizon (orange).
• Figure 2: dS$_2$ as a unit hyperboloid in 3D Minkowski space, as seen from two different perspectives. The coordinate $T$ describes the "height" along the hyperboloid while the coordinates $(X, Y)$ parameterize the circle of radius $\sqrt{1 + T^2}$ at a given $T$. The intersection of the hyperboloid with the plane $X = 1$ (orange) is the horizon of a static patch. Other horizons and static patches are related to this one by actions of the $O(2,1)$ isometry group.
• Figure 3: A plane of constant $X$ intersects the sphere on a circle of constant dilaton.
• Figure 4: The dS$_2$ hyperboloid and its intersection with various planes of constant $X$ as seen from two perspectives ("from the side" and "head on"). The orange plane is at $X=1$; its intersection with the hyperboloid forms two null lines (orange) which are the horizons of a static patch. For $|X|<1$ the intersections are timelike and shown in green. For $|X|>1$ they are spacelike and shown in red.
• Figure 5: Conformal diagram of dS$_2$ showing the lines of constant dilaton and the two antipodal static patches (regions where the surfaces of constant dilaton are timelike/green). The diagram should be understood to be periodic in the horizontal direction.