标题： 关于与二维引力耦合的顶点模型的施温格-戴森方程 显示英文标题

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

摘要： 我们考虑一个具有高斯相互作用的两矩阵模型，其中包含项$tr ABAB$，该项在角变量中是四次的。 它描述了一个在随机几何晶格上的顶点模型（特别是F型模型），是描述一般顶点模型与二维引力耦合的矩阵模型类别的最简单代表。 这类模型包括大多数物理上有意义的矩阵模型，例如格点规范理论和描述外在曲率弦的矩阵模型。 我们证明该模型的环（施温格-戴森）方程组在平面极限下解耦，并允许找到任意关联函数的闭合方程，包括涉及角变量的关联函数。 这提供了该模型在平面极限下的解。 我们写出两点函数和本征值密度的方程，并简要说明自由情况下的微扰修正计算。 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.