论文标题
量子三角形和虚构的几何流量线
Quantum triangles and imaginary geometry flow lines
论文作者
论文摘要
我们在liouville量子重力（LQG）中定义了一个三参数的随机表面家族，可以将其视为三角形的量子版本。这些量子三角形在两种感觉上是自然的。首先，根据我们的定义，它们产生了磁盘上liouville共形场理论的边界三点相关函数。其次，事实证明，这些量子三角形给出了由假想几何与LQG结合的流动线界定的三角形定律。在本文中，我们演示了量子磁盘上边界流线的第二点。我们的方法有可能以任意方式胶粘的量子三角形证明一般的保形焊接结果。量子三角形在通过共形焊接中理解SLE和LQG的整合性方面起着基本作用。在本文中，我们使用量子三角形和两点量子磁盘的共形焊接来推断具有三个力点的弦弦SLE的可集成性结果。在随后的工作中，我们将探索它们在LQG交配框架框架上的应用，包括对偏度布朗尼定位物中反转比例的确切评估。
We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natural in two senses. First, by our definition they produce the boundary three-point correlation functions of Liouville conformal field theory on the disk. Second, it turns out that the laws of the triangles bounded by flow lines in imaginary geometry coupled with LQG are given by these quantum triangles. In this paper we demonstrate the second point for boundary flow lines on a quantum disk. Our method has the potential to prove general conformal welding results with quantum triangles glued in an arbitrary way. Quantum triangles play a basic role in understanding the integrability of SLE and LQG via conformal welding. In this paper, we deduce integrability results for chordal SLE with three force points, using the conformal welding of a quantum triangle and a two-pointed quantum disk. In a subsequent work we will explore their applications to the mating-of-trees framework of LQG, including the exact evaluation of the expected proportion of inversions in skew Brownian permutons.
