论文标题
Liouville CFT的环上的共形启动
Conformal Bootstrap on the Annulus in Liouville CFT
论文作者
论文摘要
本文是Liouville Condormal Field Theory（CFT）中的一系列关于保形自举的作品的作品。我们在这里将其重点放在环形的情况下，其中有两个边界插入，每个边界插入都在边界的不同连接组件上。在证明自举公式的过程中，我们在相应的环形块上建立了几个属性： 1）我们证明它们在光谱线上到处都会收敛，并且相对于光谱和主要重量是连续的。 2）我们通过严格实施Cardy的双重技巧来将它们与他们的圆环相关联 3）我们在环形分区函数上解决了马丁内克的猜想， 4）我们还将引导程序公式扩展到单点。 作为引导结果的应用，当$γ\ in（0,2）$ in（0,2）$时，我们给出了环形液体LQG分区功能的精确公式。我们的论文是最新衍生的Brownian Annulus，Ang，Remy和Sun（2022）的Brownian Annulus的关键要素。我们还解决了其他几种猜想与物理文献产生的圆环结构块有关。
This paper is the first of a series of works on the conformal bootstrap in Liouville conformal field theory (CFT) with boundaries. We focus here on the case of the annulus with two boundary insertions, each of which lies on the different connected components of the boundary. In the course of proving the bootstrap formula, we established several properties on the corresponding annulus conformal blocks: 1) we show that they converge everywhere on the spectral line and they are continuous with respect to the spectrum and the primary weights. 2) we relate them to their torus counterparts by rigorously implementing Cardy's doubling trick for boundary CFT, 3) we solve a conjecture of Martinec on the annulus partition function, 4) we also extend the bootstrap formula to the one-point case. As an application of our bootstrap result, we give an exact formula for the bosonic LQG partition function of the annulus when $γ\in (0,2)$. Our paper serves as a key ingredient in the recent derivation of the random moduli for the Brownian annulus by Ang, Remy, and Sun (2022). We also solve several other conjectures relate to torus conformal blocks which arise from physics literature.
