论文标题
DS JT重力和双刻度SYK
dS JT Gravity and Double-Scaled SYK
论文作者
论文摘要
本文推动了[1]中提出的猜想，即Syk模型的高温双尺度极限（$ \ Mathrm {dssyk} _ {\ infty} $）描述了一个类似于保姆的空间。我们确定了一种特定的散装理论，我们认为，我们认为是$ \ mathrm {dssyk} _ {\ infty} $，即带正宇宙常数的JT重力（DS-JT）。我们将注意力集中在DS-JT的特定解决方案上，其中时空是DS $ _2 $的特定有限的子手机，Dilaton的轮廓与静态贴片的径向坐标相吻合。该解决方案可以理解为DS $ _3 $的维度减少，并且以前在[2]的情况下研究了与我们不同的上下文。我们详细描述了该解决方案的几何形状，并讨论了该解决方案的物理学与$ \ mathrm {dssyk} _ {\ infty} $相匹配的某些方法。我们描述了全息散装出现的示例，并找到了时间尺度$ t_* \ simβ_ {\ mathrm {gh}} \ log（s）$的新角色，作为管理这种出现的时间表。我们讨论了关于边界对运算符映射的一些限制。本文为L. Susskind提供的同伴论文[3]提供了其他背景和上下文，该论文将同时出现。
This paper pushes forward a conjecture made in [1] that a high-temperature double-scaled limit of the SYK model ($\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.
