All genus correlation functions for the hermitian 1-matrix model

TL;DR

This paper develops a method to compute all genus correlation functions of the hermitian 1-matrix model using residues on a hyperelliptical curve, represented diagrammatically as Feynman graphs.

Contribution

It introduces a new approach to calculate all orders of correlation functions via residues on a hyperelliptical curve, linking matrix models to diagrammatic Feynman graph representations.

Findings

All correlation functions can be computed as residues on a hyperelliptical curve.

Correlation functions are represented diagrammatically as Feynman graphs.

The method applies to all orders in the topological $1/N^2$ expansion.

Abstract

We rewrite the loop equations of the hermitian matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological $1/N^2$ expansion, as residues on an hyperelliptical curve. Those residues, can be represented diagrammaticaly as Feynmann graphs of a cubic interaction field theory on the curve.