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Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model

机译：矩阵模型的划分函数是弦论的第一个特殊函数：有限厄米单矩阵模型

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Although matrix model partition functions do not exhaust the entire set of tau-functions relevant for string theory, they are elementary blocks for constructing many other tau-functions and seem to capture the fundamental nature of quantum gravity and string theory properly. We propose taking matrix model partition functions as new special functions. This means that they should be investigated and represented in some standard form without reference to particular applications. At the same time, the tables and lists of properties should be sufficiently full to exclude unexpected peculiarities appearing in new applications. Accomplishing this task requires considerable effort, and this paper is only a first step in this direction. We restrict our consideration to the finite Hermitian one-matrix model and concentrate mostly on its phase and branch structure that arises when the partition function is considered as a D-module. We discuss the role of the CIV-DV prepotential (which generates a certain basis in the linear space of solutions of the Virasoro constraints, although an understanding of why and how this basis is distinguished is lacking) and evaluate several first multiloop correlators, which generalize the semicircular distribution to the case of multitrace and nonplanar correlators.
机译：尽管矩阵模型划分函数并未穷尽与弦理论相关的整套tau函数，但它们是构造许多其他tau函数的基本模块，并且似乎正确地把握了量子引力和弦论的基本性质。我们建议将矩阵模型分区函数作为新的特殊函数。这意味着应该对它们进行调查，并以某种标准形式表示它们，而不必参考特定的应用程序。同时，属性的表和列表应足够完整，以排除出现在新应用程序中的意外特性。完成此任务需要付出巨大的努力，而本文只是朝这个方向迈出的第一步。我们将考虑范围限制在有限的Hermitian一矩阵模型上，并且主要集中在将分区函数视为D模块时出现的相和分支结构。我们讨论了CIV-DV势的作用（尽管缺乏对为何和如何区分该基础的理解，但它在Virasoro约束的线性解决方案的空间中生成了一定的基础），并评估了多个第一个多环相关器，多迹和非平面相关器情况下的半圆形分布。

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