论文标题
矩阵型号的新Instantons
New Instantons for Matrix Models
论文作者
论文摘要
随机矩阵模型的完整，非扰动的内容由复兴的透射式描述 - 对其相应的字符串方程式的一般解决方案。这些跨系列包括通过特征值隧道获得的指数抑制的多in-Instanton振幅，但它们还包含指数增强和混合偶然的类似于矩阵的扇形，没有已知的矩阵模型解释。这项工作表明了如何通过基质模型中的特征值隧道来描述这些扇区 - 但在频谱曲线的非物理表上描述了它们的大N极限。这张照片进一步解释了通过分析所有可能的特征值集成库来解释随机矩阵的全部复兴。如何计算这些“抗”特征值隧道振幅，并在各种示例中进行了解释，例如立方和四分之一的矩阵模型，以及它们对Painleve I的双重尺度限制。这进一步提供了直接的矩阵模型衍生物的直接矩阵模型衍生物，这些矩阵模型是其旋转Stokes数据的最近获得了不同技术，这些数据是通过不同技术获得的。
The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models -- but on the non-physical sheet of the spectral curve describing their large-N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these "anti" eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.
