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, 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.

我们研究了具有固定长度边界的空间的二维Liouville重力和最小弦理论。我们发现了描述磁盘中体积和边界相关器的重力修整的显式公式。它们的结构与2d BF（加上边界项）中的可观察到的惊人相似，这与SL（2 ， ℝ）的量子变形有关，我们对此进行了详细的介绍。对于（2 ，p）最小字符串理论，我们将连续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限制相关器与Jackiw-Teitelboim重力匹配。我们考虑了使用Weil-Petersson体积的量子变形和胶合量度来胶合大量单点函数而编写的多边界振幅。派生零Weil-Petersson体积的生成函数，取大p极限。最后，我们提供了初步的证据，即本体理论可以解释为具有正Φdilaton势的二维dilaton重力模型。