Quiver matrix model and topological partition function in six dimensions
Quiver matrix model and topological partition function in six dimensions
复制标题
DOI：
10.1088/1126-6708/2009/07/076
复制
发表时间：
2009-07-01
影响因子：
5.4
通讯作者：
Kanno, Hiroaki
中科院分区：
文献类型：
--
作者：
Awata, Hidetoshi;Kanno, Hiroaki
我们考虑一个拓扑箭图矩阵模型，它有望给出D6膜上拓扑U(N)规范理论的瞬子动力学的对偶描述。该模型是引入奈克拉索夫配分函数的ADHM矩阵模型的高维类比。模空间上的环面作用的不动点用有色平面划分表示。在假设局部化定理的情况下，我们将配分函数计算为等变指标。结果表明，配分函数不依赖于希格斯场的真空期望值，希格斯场在低能时将U(N)对称性破坏为U(1)(N)。我们猜想了配分函数的一般公式，如果我们施加Calabi-Yau条件，它将降为MacMahon函数的幂。对于非Calabi-Yau情形，我们在瞬子展开式中证明了直到三阶的猜想。
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.