Quiver Matrix Model and Topological Partition Function in Six Dimensions

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.

29 pages, no figure; (v2) Proofs in section 4 improved, Appendix B revised; (v3) minor changes, references added and updated

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• Higher rank K-theoretic Donaldson-Thomas theory of points
• Entropy spectra of black holes from resonance modes in scattering by the black holes
• Tetrahedron instantons
• Orthogonal Polynomials in Mathematical Physics
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
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• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
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• Tetrahedron instantons in Donaldson-Thomas theory
• Noncommutative Instantons in Diverse Dimensions
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• N=4 Instanton Calculus in Omega and R-R Backgrounds
• Seven-dimensional super Yang-Mills at negative coupling
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• M theory and the Coulomb phase of higher rank DT invariants
• Stringy Instanton Counting and Topological Strings
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions