dS JT Gravity and Double-Scaled SYK
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916147896516608 |
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| author | Rahman, Adel A. |
| author_facet | Rahman, Adel A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_09997 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | dS JT Gravity and Double-Scaled SYK Rahman, Adel A. High Energy Physics - Theory 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. |
| title | dS JT Gravity and Double-Scaled SYK |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2209.09997 |