Loop Equations for the d-dimensional One-Hermitian Matrix model

TL;DR

This paper derives the loop equations for the d-dimensional one-Hermitian matrix model from Schwinger-Dyson equations, showing that at large N, these equations form a closed set, advancing theoretical understanding of matrix models.

Contribution

It extends the derivation of loop equations to d-dimensional Hermitian matrix models and demonstrates their closure at leading order in large N.

Findings

Loop equations derived from Schwinger-Dyson equations.

At large N, loop equations form a closed set.

Provides a framework for analyzing d-dimensional matrix models.

Abstract

We derive the loop equations for the one Hermitian matrix model in any dimension. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large $N$ the loop equations form a closed set.