Loop equations for generalised eigenvalue models

Abstract

We derive the loop equation for the 1-matrix model with generic difference-type measure for eigenvalues and develop a recursive algebraic framework for solving it to an arbitrary order in the coupling constant in and beyond the planar approximation. The planar limit is solved exactly for a one-parametric family of models and in the general case at strong coupling. The Wilson loop in the \mathcal{N}=2^*𝒩=2* super-Yang-Mills theory and the Hoppe model are used to illustrate our methods.