# Quiver Matrix Model and Topological Partition Function in Six Dimensions

@article{Awata2009QuiverMM, title={Quiver Matrix Model and Topological Partition Function in Six Dimensions}, author={Hidetoshi Awata and Hiroaki Kanno}, journal={Journal of High Energy Physics}, year={2009}, volume={2009}, pages={076-076} }

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…

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## References

SHOWING 1-10 OF 46 REFERENCES

### Instanton counting, Macdonald function and the moduli space of D-branes

- Mathematics
- 2005

We argue the connection of Nekrasov's partition function in the Ω background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the…

### Topological Quiver Matrix Models and Quantum Foam

- Mathematics
- 2007

We study the matrix models that describe the BPS bound states of branes arising from the quiver picture of the derived category. These theories have a topological partition function that localizes to…

### Small Instantons, Little Strings and Free Fermions

- Physics, Mathematics
- 2003

We present new evidence for the conjecture that BPS correlation functions in the N=2 supersymmetric gauge theories are described by an auxiliary two dimensional conformal field theory. We study…

### The Topological Vertex

- Mathematics, Physics
- 2005

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the…

### Refined Topological Vertex and Instanton Counting

- Mathematics
- 2008

It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is…

### Instantons and the 5D U(1) gauge theory with extra adjoint

- Mathematics
- 2009

In this paper, we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general Ω background. It is well known that such partition functions encode very…

### Instanton Counting and Chern-Simons Theory

- Physics
- 2002

The instanton partition function of N = 2, D = 4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of…

### Special Quantum Field Theories¶in Eight and Other Dimensions

- Physics
- 1997

Abstract:We build nearly topological quantum field theories in various dimensions. We give special attention to the case of eight dimensions for which we first consider theories depending only on…

### SU(N) Geometries and Topological String Amplitudes

- Mathematics, Physics
- 2003

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3folds giving rise to N = 2…