Conformal blocks and Painlev\'e functions
Conformal blocks and Painlev\'e functions
复制标题
DOI：
--
复制
发表时间：
2016-11
期刊：
影响因子：
--
通讯作者：
H. Nagoya
中科院分区：
文献类型：
--
作者：
H. Nagoya
这篇论文是基于我在2015年8月19- 21日在京都举行的RIMS研讨会上的“可积分系统理论及其在各个领域的应用”的演讲。本文的目的是简要介绍二维共形场理论中共形块与Painlev函数之间关系的最新研究。此外，我们给出了具有两个正则奇点和一个不规则奇点的三点不规则共形块的组合展开公式的一个猜想。我们的推测展开公式是用一对斜杨图来表示的，而四点正则共形块，通过AGT对应，是用一对杨图来表示的。
This paper is based on my presentation at RIMS workshop on "Theory of Integrable Systems and Its Applications in Various Fields" held in Kyoto on 19--21, August 2015. The aim of the present paper is to give a short account of recent studies on relations between conformal blocks in the two-dimensional conformal field theory and Painlev\'e functions. In addition, we present a conjecture on a combinatorial expansion formula of the three-point irregular conformal block at an irregular singular point, with two regular singular points and one irregular singular point. Our conjectural expansion formula is written in terms of pairs of skew Young diagrams, while the four-point regular conformal block, by AGT correspondence, is written in terms of pairs of Young diagrams.