论文标题
$ t^2 $变形的重力路径积分
Gravitational path integral from the $T^2$ deformation
论文作者
论文摘要
我们研究了$ t $ n $共形的场理论的$ t^2 $变形，$ t \ bar t $变形的较高维度概括。变形分区函数满足扩散类型的流程方程。我们通过找到其扩散核来求解该方程，该方程是由欧几里得重力路径积分在$ d+1 $尺寸中的$ d+1 $尺寸中给出的。鉴于流程方程与惠勒 - 戴维特方程之间的联系是自然的，我们通过在变形的分区函数与径向WDW波函数之间提供量规不变的关系来提供新的视角。流程方程的一个有趣的输出是重力路径积分度量，它与约束相空间量化一致。最后，我们评论了径向波函数与CFT中的状态双重双重函数之间的关系，并提出了一种从$ t^2 $变形中获取最大切片体积的方法。
We study a $T^2$ deformation of large $N$ conformal field theories, a higher dimensional generalization of the $T\bar T$ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is given by the Euclidean gravitational path integral in $d+1$ dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the $T^2$ deformation.
