Matrix model from $ \mathcal{N} = 2 $ orbifold partition function

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.