Matrix Models of 2D Gravity and Induced QCD

TL;DR

This paper reviews recent developments in matrix models of 2D gravity and induced QCD, focusing on large-N solutions, higher genus calculations, and fermionic models, with implications for quantum field theory.

Contribution

It provides new solutions for large-N matrix models, including higher genus calculations and the large-N solution for a logarithmic potential.

Findings

Large-N solutions for Hermitean one-matrix models

Higher genus calculations in matrix models

Large-N solution for logarithmic potential

Abstract

I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns calculations of higher genera, while for the d-dimensional model the large-N solution for a logarithmic potential is described. Some results on fermionic matrix models are briefly reviewed. Talk at the Workshop on Quantum Field Theoretical Aspects of High Energy Physics, Kyffhaeuser, Germany, September 20-24, 1993