Quiver Matrix Model and Topological Partition Function in Six Dimensions

TL;DR

This paper introduces a topological quiver matrix model in six dimensions that generalizes the ADHM model, computes its partition function via localization, and explores its relation to the MacMahon function under Calabi-Yau conditions.

Contribution

It proposes a new six-dimensional quiver matrix model for D6 branes, computes the partition function using localization, and conjectures a formula linking it to the MacMahon function.

Findings

Partition function independent of Higgs VEVs.

Conjectured formula reduces to MacMahon function under Calabi-Yau condition.

Proved the conjecture up to third order in instanton expansion for non Calabi-Yau case.

Abstract

We consider a topological quiver matrix model which is expected to give a dual description of the instanton dynamics of topological U(N) gauge theory on D6 branes. The model is a higher dimensional analogue of the ADHM matrix model that leads to Nekrasov's partition function. The fixed points of the toric action on the moduli space are labeled by colored plane partitions. Assuming the localization theorem, we compute the partition function as an equivariant index. It turns out that the partition function does not depend on the vacuum expectation values of Higgs fields that break U(N) symmetry to U(1)^N at low energy. We conjecture a general formula of the partition function, which reduces to a power of the MacMahon function, if we impose the Calabi-Yau condition. For non Calabi-Yau case we prove the conjecture up to the third order in the instanton expansion.