Loop Equations for the d-dimensional n-Hermitian matrix model

TL;DR

This paper derives loop equations for a d-dimensional n-Hermitian matrix model, showing they form a closed set at large N and applying to models coupling 2D quantum gravity with conformal matter.

Contribution

It introduces the derivation of loop equations for the d-dimensional n-Hermitian matrix model and demonstrates their closure at leading order in large N, including specific cases relevant to quantum gravity.

Findings

Loop equations are derived from Schwinger-Dyson equations.

At large N, loop equations form a closed set.

Application to models coupling 2D quantum gravity with conformal matter.

Abstract

We derive the loop equations for the d-dimensional n-Hermitian matrix model. 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. In particular we derive the loop equations for the $n=2^k$ matrix model recently proposed to describe the coupling of Two-dimensional quantum gravity to conformal matter with $c> 1$.