标题： 关于具有对数势的艾里矩阵模型 显示英文标题

标题： On an Airy matrix model with a logarithmic potential

摘要： Kontsevich-Penner模型，一个具有对数势的Airy矩阵模型，可以通过对偶性从一个简单的高斯双矩阵模型导出。 在这个对偶版本中，n点关联函数的傅里叶变换可以以闭合形式计算。 使用Virasoro约束，我们发现除了在KdV层次结构中出现的参数$t_n$外，还需要在这里引入半整数索引$t_{n/2}$。 作为这些参数的函数的自由能可以从这些Virasoro约束中获得。 大N极限来自于积分方程的解。 这导致了许多拓扑不变量的显式计算。 显示英文摘要

摘要： The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can be computed in closed form. Using Virasoro constraints, we find that in addition to the parameters $t_n$, which appears in the KdV hierarchies, one needs to introduce here half-integer indices $t_{n/2}$ . The free energy as a function of those parameters may be obtained from these Virasoro constraints. The large N limit follows from the solution to an integral equation. This leads to explicit computations for a number of topological invariants.