论文标题
$ \ mathfrak {sl} _3 $ toda理论I I：反射系数中的三点相关功能
Three-point correlation functions in the $\mathfrak{sl}_3$ Toda theory I: Reflection coefficients
论文作者
论文摘要
TODA保形场理论（CFTS）构成了由半神经和复杂的代数索引的2D CFT家族。它们是Liouville CFT的自然概括，因为它们享有由W-Algebras编码的增强的对称水平。这些理论可以使用概率框架进行严格定义，该概率框架涉及相关的高斯乘法混乱度量。 该文档提供了朝着计算一类三点相关函数的第一步，该功能概括了著名的dozz公式，并且在与$ \ mathfrak {sl} _3 _3 _3 $ toda cft相关的概率框架内，Fateev-Litvinov在物理文献中预测其表达方式。即，两部分系列的第一篇文章致力于一般TODA CFT的反射系数的概率推导，这在理解TODA相关函数时是必不可少的基础。 沿着这些反射系数的计算，基于适当的最小值概念，将在欧几里得空间中扩散过程的新路径分解，并将推出威廉姆斯的著名一维结果。作为副产品，我们描述了相关高斯乘法混乱的关节尾膨胀以及一级惠特克函数的渐近扩展。
Toda Conformal Field Theories (CFTs) form a family of 2d CFTs indexed by semisimple and complex Lie algebras. They are natural generalizations of the Liouville CFT in that they enjoy an enhanced level of symmetry encoded by W-algebras. These theories can be rigorously defined using a probabilistic framework that involves the consideration of correlated Gaussian Multiplicative Chaos measures. This document provides a first step towards the computation of a class of three-point correlation functions, that generalize the celebrated DOZZ formula and whose expressions were predicted in the physics literature by Fateev-Litvinov, within the probabilistic framework associated to the $\mathfrak{sl}_3$ Toda CFT. Namely this first article of a two-parts series is dedicated to the probabilistic derivation of the reflection coefficients of general Toda CFTs, which are essential building blocks in the understanding of Toda correlation functions. Along the computations of these reflection coefficients a new path decomposition for diffusion processes in Euclidean spaces, based on a suitable notion of minimum and that generalizes the celebrated one-dimensional result of Williams, will be unveiled. As a byproduct we describe the joint tail expansion of correlated Gaussian Multiplicative Chaos measures together with an asymptotic expansion of class one Whittaker functions.
