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 N=2* super-Yang-Mills theory and the Hoppe model are used to illustrate our methods.

61 pages, 6 figures, Mathematica notebooks with perturbative solution of loop equations are included as ancillary files; v2: refs added; v3: more refs added

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