Renormalization Group Approach to Matrix Models

TL;DR

This paper develops a renormalization group framework for matrix models of 2D quantum gravity, providing an approximate method to understand both solvable and unsolved cases by analyzing parameter flows.

Contribution

It introduces a renormalization group approach to matrix models, enabling qualitative analysis of models beyond exactly solvable cases.

Findings

Reproduces qualitative properties of $ c extless=1 $ models

Constructs RG equations at lowest orders

Provides a new tool for studying matrix models

Abstract

Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be carried to the unsolved cases in order to achieve at least a qualitative understanding of the properties of the models. The double scaling limit is an indication that a change of the length scale induces a flow in the parameters of the theory, the size of the matrix and the coupling constants for matrix models, at constant long distances physics. We construct here these renormalization group equations at lowest orders in various cases to check that we reproduce qualitatively the properties of $ c\leq 1 $ models.