Renormalization Group Approach to Matrix Models in Two-Dimensional Quantum Gravity

TL;DR

This paper applies renormalization group techniques to matrix models in two-dimensional quantum gravity, analyzing fixed points and perturbative expansions to understand critical behavior.

Contribution

It introduces a renormalization group framework to study matrix models in 2D quantum gravity, providing insights into fixed points and perturbative corrections.

Findings

Leading order results match saddle-point approximation

Next-to-leading order calculations explore perturbative approach validity

Renormalization group methods offer a new perspective on critical points

Abstract

We explore the implications of recent work by Br\'ezin and Zinn-Justin, applying the renormalization group techniques from critical phenomena to the scaling limit of matrix models in two-dimensional quantum gravity. They endeavor to get the lowest order fixed points of the theory giving insight upon the critical points of the theory. We show that at leading order the perturbative result is equal to the saddle-point approximation result. We calculate the next-to-leading order in the perturbative expansion exploring the goodness of the approach.