Les Houches lectures on matrix models and topological strings

TL;DR

This paper introduces the relationship between matrix models and topological strings, highlighting their role in understanding string dynamics, geometric transitions, and gauge/string duality, with applications to Chern-Simons theory.

Contribution

It provides an overview of matrix model techniques applied to topological strings and discusses key results connecting these models to string theory and gauge theories.

Findings

Matrix models describe spacetime string dynamics on Calabi-Yau backgrounds.

Connection established between matrix models and geometric transitions.

Analysis of large N Chern-Simons theory and Gopakumar-Vafa transition using matrix technology.

Abstract

In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model technology and then we focus on type B topological strings. We present the main results of Dijkgraaf and Vafa describing the spacetime string dynamics on certain Calabi-Yau backgrounds in terms of matrix models, and we emphasize the connection to geometric transitions and to large N gauge/string duality. We also use matrix model technology to analyze large N Chern-Simons theory and the Gopakumar-Vafa transition.