Beta-ensembles for toric orbifold partition function

TL;DR

This paper explores the combinatorial structure of instanton partition functions on toric orbifolds, revealing how orbifold projections relate to root of unity limits and deriving a multi-matrix model for arbitrary beta.

Contribution

It introduces a novel approach to implement orbifold projections via inhomogeneous root of unity limits of q-deformed functions and derives a multi-matrix model for generic beta.

Findings

Orbifold projection corresponds to root of unity limit of q-deformed partition functions.

Asymptotics lead to a multi-matrix model for arbitrary beta.

Provides new combinatorial insights into instanton partition functions on toric orbifolds.

Abstract

We investigate combinatorics of the instanton partition function for the generic four dimensional toric orbifolds. It is shown that the orbifold projection can be implemented by taking the inhomogeneous root of unity limit of the q-deformed partition function. The asymptotics of the combinatorial partition function yields the multi-matrix model for a generic $\beta$.