Instanton Counting and Matrix Model

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 $\mathcal{N}=2$ 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.

14 pages; v2: references added and typos fixed

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