论文标题
Annuli的模量随机保形几何形状
The moduli of annuli in random conformal geometry
论文作者
论文摘要
我们获得了取决于环的模量的随机共形几何形状中三个基本量的精确公式。首先是用于布朗环的模量定律，该定律描述了带有环形拓扑的均匀采样平面图的缩放限制，这是从幽灵分区函数中预测的，在Bosonic String理论中。第二个是为环形模量定律，该定律是由磁盘和磁盘边界上简单的形条环（CLE）的环界定的。该公式是从Saleur-Bauer（1989）和Cardy（2006）衍生的环上的O $（n）$ loop模型的分区功能的猜想。第三是用于SLE $ _ {8/3} $ loop的环形分区功能，由Werner（2008）引入，{确认Cardy（2006）的另一个}预测。我们证明的物理原理是2D量子重力加上共形物质可以分解为三种形式的田野理论（CFT）：CFT，Liouville CFT和Ghost CFT。在技术层面上，我们依靠Liouville量子重力中的两种可集成性，一个是从随机平面图的缩放限制中，另一种来自Liouville CFT。
We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The first is for the law of the modulus of the Brownian annulus describing the scaling limit of uniformly sampled planar maps with annular topology, which is as predicted from the ghost partition function in bosonic string theory. The second is for the law of the modulus of the annulus bounded by a loop of a simple conformal loop ensemble (CLE) on a disk and the disk boundary. The formula is as conjectured from the partition function of the O$(n)$ loop model on the annulus derived by Saleur-Bauer (1989) and Cardy (2006). The third is for the annulus partition function of the SLE$_{8/3}$ loop introduced by Werner (2008), {confirming another} prediction of Cardy (2006). The physics principle underlying our proofs is that 2D quantum gravity coupled with conformal matters can be decomposed into three conformal field theories (CFT): the matter CFT, the Liouville CFT, and the ghost CFT. At the technical level, we rely on two types of integrability in Liouville quantum gravity, one from the scaling limit of random planar maps, the other from the Liouville CFT.
