Proof of the Lagrangean formalism of Hermitean 1-matrix models to all orders

TL;DR

This paper demonstrates that the correlation functions and free energy of Hermitean 1-matrix models can be fully described by a Lagrangean formalism, with explicit solutions to loop equations up to fifth order in 1/N^2.

Contribution

It establishes the all-order validity of the Lagrangean formalism for Hermitean 1-matrix models and explicitly solves loop equations up to fifth order.

Findings

Lagrangean formalism describes correlation functions and free energy to all orders

Loop equations are explicitly solved up to fifth order in 1/N^2

Provides a framework for analyzing Hermitean 1-matrix models

Abstract

We show that the correlation functions and the free energy of the formal Hermitean 1-matrix model can be described by the recently proposed Lagrangean formalism to all orders. In addition, the loop equation of this formalism is stated and solved up to the fifth order in 1 / N^2 explicitly.