  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.
