Matrix model from N = 2 orbifold partition function

TL;DR

This paper explores the orbifold generalization of gauge theory partition functions, deriving a new multi-matrix model and connecting it to Seiberg-Witten curves through combinatorial and asymptotic analysis.

Contribution

It introduces a novel multi-matrix model from the orbifold partition function and links it to the Seiberg-Witten curve via spectral analysis.

Findings

Root of unity limit is crucial for orbifold projection

Derived a new multi-matrix model from combinatorial representation

Connected spectral curve of the matrix model to Seiberg-Witten curve

Abstract

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function plays a crucial role on the orbifold projection. Then starting from the combinatorial representation of the partition function, a new type of multi-matrix model is derived by considering its asymptotic behavior. It is also shown that Seiberg-Witten curve for the corresponding gauge theory arises from the spectral curve of this multi-matrix model.