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dS JT Gravity and Double-Scaled SYK
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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 $t_* \sim \beta_{\mathrm{GH}}\log(S)$ 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.
Forward citations
Cited by 5 Pith papers
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Negative shocks versus static patch holography
Out-of-time-order correlators along a de Sitter observer worldline, computed with the shockwave eikonal formalism including recoil and backreaction, violate the cyclicity and positivity required of a trace, falsifying...
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De Sitter Complexity Grows Linearly in the Static Patch
Timelike extremal volume in the de Sitter static patch gives a holographic complexity that grows linearly with time and is proportional to horizon entropy times temperature.
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A microscopic model of de Sitter spacetime with an observer
The entropy of a Schwarzschild-de Sitter universe with an observer matches the spectral entropy of double-scaled SYK once the coupling is set to 8πG_N, explaining the model's two temperatures.
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A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification
The claimed RL safety verification framework is absent from the manuscript; the body text is an unrelated high-energy physics paper about de Sitter horizon chaos.
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