Advances in Large N Group Theory and the Solution of Two-Dimensional R^2 Gravity

TL;DR

This paper presents a new large N technique for matrix models and applies it to solve two-dimensional R^2 gravity, providing new insights into quantum gravity in two dimensions.

Contribution

It introduces a novel large N method for complex matrix models and offers the first precise analysis of two-dimensional R^2 gravity.

Findings

Development of a new large N technique for matrix models

Exact solution of a matrix model interpolating between flat and random lattices

First precise statement about two-dimensional R^2 gravity

Abstract

We review the recent exact solution of a matrix model which interpolates between flat and random lattices. The importance of the results is twofold: Firstly, we have developed a new large N technique capable of treating a class of matrix models previously thought to be unsolvable. Secondly, we are able to make a first precise statement about two-dimensional R^2 gravity. These notes are based on a lecture given at the Cargese summer school 1995. They contain some previously unpublished results.