Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
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ADHM型箭袋矩阵模型及多维BPS状态计数
DOI：
10.1093/ptep/ptaa079
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发表时间：
2020
影响因子：
3.5
通讯作者：
Kanno Hiroaki
中科院分区：
文献类型：
--
作者：
Yasuhiro Hara;Masaharu Morimoto;Kanno Hiroaki
讨论了用广义颤振矩阵模型（Atiyah-Drinfield-Hitchin-Manin型）描述的Bogomol 'nyi-Prasad-Sommerfield （BPS）状态计数问题。在四维中，计数的生成函数给出涅克拉索夫配分函数，并在高维中得到推广。根据局部化定理，配分函数由环面作用的不动点贡献的和给出，用分区、平面分区和实体分区来标记。路径积分的度量或玻尔兹曼权值可以采用多体指数的形式。值得注意的是，积分后的配分函数或真空期望值再次以多面体形式表示。我们把它看作是与可积性密切相关的BPS状态计数问题的一个特征性质。
We review the problem of Bogomol’nyi–Prasad–Sommerfield (BPS) state counting described by the generalized quiver matrix model of Atiyah–Drinfield–Hitchin–Manin type. In four dimensions the generating function of the counting gives the Nekrasov partition function, and we obtain a 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.