论文标题
liouville量子重力 - 全息，JT和矩阵
Liouville quantum gravity -- holography, JT and matrices
论文作者
论文摘要
我们研究了具有固定长度边界的空间上的二维liouville重力和最小的弦理论。我们发现磁盘中散装和边界相关因子的重力敷料的明确公式。它们的结构与2D BF（加上边界项）中的可观察物具有惊人的相似之处，与$ SL（2，\ Mathbb {r}）$的量子变形相关，这是我们在一些详细范围内开发的连接。对于$（2，p）$最小的字符串理论，我们将Continuum方法的结果与矩阵模型计算进行比较和匹配，并验证在大$ p $中，相关器与Jackiw-Teitelboim Gravity匹配。我们考虑使用Weil-Petersson体积和胶合度措施的量子变形，以粘合大量的一分点功能来撰写的多边界振幅。得出了零$ p $限制的零元素属的生成功能。最后，我们提供了初步证据，表明可以将批量理论解释为具有$ \sinhφ$ dilaton潜力的2D Dilaton重力模型。
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large $p$ limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a $\sinh Φ$ dilaton potential.
