Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group

TL;DR

This paper introduces the use of the functional Renormalization Group to analyze the double-scaling limit in matrix models for 2D quantum gravity, providing a nonperturbative approach to identify fixed points and critical exponents.

Contribution

It demonstrates the application of the functional Renormalization Group to matrix models, enabling the computation of fixed points and critical exponents, and extends the method to tensor models and group field theories.

Findings

Explicit evaluation of critical exponents matching exact results

Identification of the nonperturbative fixed point in matrix models

Calculation of the leading-order beta function for a tensor-inspired matrix model

Abstract

We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the Renormalization Group flow. We explicitly evaluate critical exponents and compare to the exact results. The functional Renormalization Group method allows a generalization to tensor models for higher-dimensional quantum gravity and to group field theories. As a simple example how this method works for such models, we compute the leading-order beta function for a colored matrix model that is inspired by recent developments in tensor models.