标题： 关于与二维引力耦合的顶点模型的施温格- Dyson 方程 显示英文标题

标题： On the Schwinger-Dyson Equations for a Vertex Model Coupled to 2D Gravity

摘要： 我们考虑一个双矩阵模型，其中高斯相互作用涉及角变量的四次项$tr ABAB$。它描述了一个顶点模型（特定情况下为F-模型类型）在波动几何结构的晶格上，并且是描述一般顶点模型与二维引力耦合的矩阵模型中最简单的代表。 这一类包括大多数物理上有意义的矩阵模型，例如晶格规范理论和描述外在曲率弦的矩阵模型。 我们证明了该模型的环（施温格-狄拉克）方程在平面极限下可解耦，并允许得到任意相关函数的闭合方程，包括涉及角变量的相关函数。 这为在平面极限下解决该模型提供了方法。 我们写下了关于两点函数和特征值密度的方程，并概述了自由情况下的微扰校正计算。 显示英文摘要

摘要： We consider a two matrix model with gaussian interaction involving the term $tr ABAB$, which is quartic in angular variables. It describes a vertex model (in particular case - of F-model type) on the lattice of fluctuating geometry and is the simplest representative of the class of matrix models describing coupling to two-dimensional gravity of general vertex models. This class includes most of physically interesting matrix models, such as lattice gauge theories and matrix models describing extrinsic curvature strings. We show that the system of loop (Schwinger-Dyson) equations of the model decouples in the planar limit and allows one to find closed equations for arbitrary correlators, including the ones involving angular variables. This provides a solution of the model in the planar limit. We write down the equations for the two-point function and the eigenvalue density and sketch the calculation of perturbative corrections to the free case.