Instanton Counting and Matrix Model

TL;DR

This paper introduces a matrix model that exactly reproduces various partition functions in topological string theory, gauge theory, and Yang-Mills theory, revealing deep connections between these areas.

Contribution

It constructs a new Imbimbo-Mukhi type matrix model and proposes a dual Stieltjes-Wigert type model linking topological strings and gauge theories.

Findings

Exact reproduction of topological string partition functions

Connection between matrix models and gauge theories

Proposal of a dual matrix model for toric Calabi-Yau manifolds

Abstract

We construct an Imbimbo-Mukhi type matrix model, which reproduces exactly the partition function of ${\mathbb{CP}^1}$ topological strings in the small phase space, Nekrasov's instanton counting in ${\cal{N}}=2$ gauge theory and the large $N$ limit of the partition function in 2-dimensional Yang-Mills theory on a sphere. In addition, we propose a dual Stieltjes-Wigert type matrix model, which emerges when all-genus topological string amplitudes on certain simple toric Calabi-Yau manifolds are compared with the Imbimbo-Mukhi type model.