Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
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DOI：
10.1063/1.4937760
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发表时间：
2015-05
影响因子：
1.3
通讯作者：
H. Nagoya
中科院分区：
文献类型：
--
作者：
H. Nagoya
我们发展了 Virasoro 代数的不规则共角块理论。以往的研究中，得到了不规则共形块在规则奇点处的展开作为规则共形块的退化极限；然而，这种在不规则奇点处的展开还没有被清楚地理解。这是因为之前没有提供不规则顶点算子的精确定义。在本文中，我们提出了两种类型的不规则顶点算子的精确定义，并证明了我们的顶点算子之一是唯一存在的。然后，我们定义具有至多两个不规则奇异点的不规则共形块作为给定不规则顶点算子的期望值。我们的定义提供了对不规则共角块展开的理解，并使我们能够获得不规则奇点处的展开。作为一个应用，我们提出了第五和第四 Painleve 方程的 tau 函数的级数展开的猜想公式，使用 i 的展开...
We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painleve equations, using expansions of i...