Renormalized expansion for matrix models

TL;DR

This paper develops a renormalized perturbation approach for matrix models of 2D quantum gravity coupled with matter, using vector model representations and saddle point methods to derive the renormalization group beta-function.

Contribution

It introduces a novel renormalized perturbational framework for matrix models, connecting them to vector models and deriving the beta-function via saddle point analysis.

Findings

Beta-function obtained in successive approximation

Matrix models related to vector models through Hamiltonian representation

Provides insights into the renormalization group flow in 2D quantum gravity models

Abstract

Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the renormalization group beta-function is obtained in the successive approximation.