论文标题
ADHM类型和BPS状态计数的Quiver矩阵模型以不同的维度计数
Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
论文作者
论文摘要
我们回顾了ADHM类型的广义箭量矩阵模型所描述的BPS状态计数的问题。在四个维度中，计数的生成函数赋予了Nekrasov分区函数，我们在更高的维度中获得了概括。根据本地化定理，分区函数由圆环动作的固定点的贡献之和给出，这些贡献由分区，平面分区和实心分区标记。路径积分的度量或玻尔兹曼重量可以采取多个指数的形式。值得注意的是，在整合后，分区函数或真空期望值再次以多种形式表示。我们将其视为BPS状态计数问题的特性属性，该属性与集成性密切相关。
We review the problem of BPS state counting described by the generalized quiver matrix model of ADHM type. In four dimensions the generating function of the counting gives the Nekrasov partition function and we obtain generalization in higher dimensions. By the localization theorem, the partition function is given by the sum of contributions from the fixed points of the torus action, which are labeled by partitions, plane partitions and solid partitions. The measure or the Boltzmann weight of the path integral can take the form of the plethystic exponential. Remarkably after integration the partition function or the vacuum expectation value is again expressed in plethystic form. We regard it as a characteristic property of the BPS state counting problem, which is closely related to the integrability.
