Lectures on non-perturbative effects in large N gauge theories, matrix models and strings

TL;DR

This paper reviews non-perturbative instanton effects in large N gauge theories, matrix models, and string theory, emphasizing resurgent analysis and its applications to understanding quantum non-perturbative phenomena.

Contribution

It introduces resurgent analysis techniques to study non-perturbative effects in large N gauge theories and matrix models, providing detailed insights and applications in string theory.

Findings

Resurgent analysis elucidates instanton effects in differential equations.

Non-perturbative effects in matrix models are systematically reviewed.

Applications to string theory demonstrate the utility of these techniques.

Abstract

In these lectures I present a review of non-perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these effects in the case of ordinary differential equations, which provide a model for more complicated theories, and I introduce in a pedagogical way some technology from resurgent analysis, like trans-series and the resurgent version of the Stokes phenomenon. After reviewing instanton effects in quantum mechanics and quantum field theory, I address general aspects of large N instantons and then present a detailed review of non-perturbative effects in matrix models. Finally, I also consider two applications of these techniques in string theory