Large N Renormalization Group Approach to Matrix Models

TL;DR

This paper develops a large N renormalization group framework for matrix models related to 2D quantum gravity, deriving exact equations and identifying fixed points and scaling exponents.

Contribution

It introduces a nonlinear RG equation and an algorithm for fixed points, reproducing the spectrum of relevant operators in matrix models.

Findings

Derived exact RG equations for matrix models.

Identified fixed points and scaling exponents.

Reproduced the spectrum of relevant operators.

Abstract

We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce infinitely many induced interactions to a finite number of them. We find a nonlinear RG equation and an algorithm to obtain the fixed points and the scaling exponents. They reproduce the spectrum of relevant operators in the exact solution. The RG flow is visualized by the linear approximation.