ON THE SCHWINGER–DYSON EQUATIONS FOR A VERTEX MODEL COUPLED TO 2-D GRAVITY

Abstract

We consider a two-matrix model with the interaction involving the term tr ABAB, which is quartic in angular variables. It describes a vertex model (in particular — 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 the 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. 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