Riemann假设、矩阵/引力对应和FZZT膜配分函数
Riemann Hypothesis, Matrix/Gravity Correspondence and FZZT Brane Partition Functions
摘要：
我们调查的物理解释的黎曼zeta函数作为FZZT膜配分函数与矩阵/重力对应。在这种解释中的希尔伯特-波利亚算子是大N矩阵模型的主矩阵。使用相关函数$Ξ(z)$，我们开发了该函数与高斯矩阵模型的Airy函数Ai（z）之间的类比。这个类比给出了零点为什么位于临界线上的直观物理原因。使用$Ξ(z)$函数的傅立叶变换，我们确定Kontsevich被积函数。将此被积函数推广到$n \times n$矩阵，我们建立了一个描述n个FZZT膜的Kontsevich矩阵模型。与$Ξ(z)$函数相关联的Kontsevich模型由已用于描述矩阵模型瞬子的Liouville型矩阵模型的叠加给出。
英文摘要：
We investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence. The Hilbert-Polya operator in this interpretation is the master matrix of the large N matrix model. Using a related function $Ξ(z)$ we develop an analogy between this function and the Airy function Ai(z) of the Gaussian matrix model. The analogy gives an intuitive physical reason why the zeros lie on a critical line. Using a Fourier transform of the $Ξ(z)$ function we identify a Kontsevich integrand. Generalizing this integrand to $n \times n$ matrices we develop a Kontsevich matrix model which describes n FZZT branes. The Kontsevich model associated with the $Ξ(z)$ function is given by a superposition of Liouville type matrix models that have been used to describe matrix model instantons.
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