Exact 2-point function in Hermitian matrix model
Exact 2-point function in Hermitian matrix model
复制标题
DOI：
10.1088/1126-6708/2009/12/003
复制
发表时间：
2009-06
影响因子：
5.4
通讯作者：
A. Morozov;Shamil Shakirov
中科院分区：
文献类型：
--
作者：
A. Morozov;Shamil Shakirov
J. Harer 和 D. Zagier 发现了高斯埃尔米特矩阵模型中精确（所有属）1 点相关器的极其简单的生成函数 (1, 2)。在本文中，我们使用模型的 Toda 可积性将其结果推广到 2 点相关器。值得注意的是，这个精确的两点相关函数实际上是一个初等函数——反正切。指出了与标准两点解析的关系。描述了一些推广到 3 点及更高函数的尝试。
J. Harer and D. Zagier have found a strikingly simple generating function (1, 2) for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function — arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.