Large N Gauge Theory -- Expansions and Transitions

TL;DR

This paper explores the connection between large N gauge theories and string theory using solvable models, introduces mathematical tools for higher-dimensional theories, and derives key equations governing spectral density evolution.

Contribution

It presents new derivations and mathematical frameworks for understanding large N gauge theories and their relation to string theory, including a novel derivation of the Hopf equation.

Findings

Illustrated the relation between large N gauge theories and string theory using solvable models

Introduced mathematical methods for constructing master fields in higher dimensions

Derived the Hopf equation for spectral density evolution in matrix quantum mechanics

Abstract

We use solvable two-dimensional gauge theories to illustrate the issues in relating large N gauge theory to string theory. We also give an introduction to recent mathematical work which allows constructing master fields for higher dimensional large N theories. We illustrate this with a new derivation of the Hopf equation governing the evolution of the spectral density in matrix quantum mechanics. Based on lectures given at the 1994 Trieste Spring School on String Theory, Gauge Theory and Quantum Gravity.