Matrix Models, Topological Strings, and Supersymmetric Gauge Theories

TL;DR

This paper establishes a connection between topological string theories on Calabi-Yau manifolds, matrix models, and supersymmetric gauge theories, revealing how these frameworks interrelate through large N dualities and geometric limits.

Contribution

It demonstrates that B-model topological strings are dual to matrix models which compute gauge theory F-terms, and links non-critical strings to superstring backgrounds via geometric tuning.

Findings

Matrix models compute F-terms in N=1 gauge theories.

Large N duality relates topological strings to matrix models.

Double scaling limits connect to (p,q) minimal models and 2d gravity.

Abstract

We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.