Renormalized expansion for matrix models

TL;DR

This paper develops a renormalized perturbation approach for matrix models in 2D quantum gravity, deriving the renormalization group beta-function via saddle point analysis.

Contribution

It introduces a novel renormalized perturbational method for matrix models, connecting them to vector models and calculating the beta-function.

Findings

Beta-function derived in successive approximation

Matrix models represented as vector models

Provides insights into 2D quantum gravity coupling

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.