We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wavefunctional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the $T\overline{T}$ deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the $T\overline{T}$ deformation as the movement of the AdS boundary to a finite radial distance in the bulk.

中文翻译：

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极限截止时的JT重力

我们通过两种方式计算有限截止时2D Jackiw-Teitelboim（JT）重力的分配函数：（i）通过径向量化中的Wheeler-DeWitt波函数的精确评估，以及（ii）通过直接计算欧几里德路径积分。两种方法都处理度量和dilaton的Dirichlet边界条件。在第一种方法中，通过将约束方程式简化为两个可以精确求解的一阶函数导数方程（包括因子排序）来找到径向波函数。在第二种方法中，当对具有磁盘拓扑的表面求和时，我们精确地执行路径积分，直到截止值中的扰动理论中的所有阶次。这两个结果都精确匹配Schwarzian理论中最近导出的由运算符变形的分区函数，类似于二维CFT中的$ T \ overline {T} $变形。这种相等性可以看作是对全息图解释的具体证据，因为全息图解释了AdS边界向本体中有限的径向距离的移动。