论文标题
$ \ mathfrak {sl} _3 $ toda理论II：Fateev-Litvinov公式中的三点相关功能
Three-point correlation functions in the $\mathfrak{sl}_3$ Toda theory II: the Fateev-Litvinov formula
论文作者
论文摘要
TODA形成性场理论（CFTS）形成了由半含量和复杂的代数索引的二维CFT家族。他们的非凡特征之一是，它们是liouville CFT的天然概括，它具有增强的对称水平，由$ w $ - 代数所规定。他们同样，就高斯乘法混乱而言，承认概率的表述。 基于这个概率框架，两部分系列中的第二篇文章致力于为这些理论的综合性提供第一步。从这个角度来看，我们证明了与$ \ mathfrak {sl} _3 $ toda cft相关的三点相关函数系列的Fateev-Litvinov公式。这个结果是Liouville CFT中著名的Dozz公式的类似物。我们的证明特征方法灵感来自物理学文献的启发，以及在Toda理论的环境中自然出现的概率。
Toda Conformal Field Theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras. One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced level of symmetry, prescribed by $W$-algebras. They likewise admit a probabilistic formulation in terms of Gaussian Multiplicative Chaos. Based on this probabilistic framework, this second article in a two-part series is dedicated to providing a first step towards integrability of these theories. In this perspective we prove the Fateev-Litvinov formula for a family of three-point correlation functions associated to the $\mathfrak{sl}_3$ Toda CFT. This result is the analog of the celebrated DOZZ formula in Liouville CFT. Our method of proof features techniques inspired by the physics literature together with probabilistic ones that naturally arise within the setting of Toda theories.
