Localization on the D-brane, two-dimensional gauge theory and matrix models
Localization on the D-brane, two-dimensional gauge theory and matrix models
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D 膜、二维规范理论和矩阵模型的定位
DOI：
10.1103/physrevd.73.046006
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发表时间：
2005
影响因子：
5
通讯作者：
Kazutoshi Ohta
中科院分区：
文献类型：
--
作者：
So Matsuura;Kazutoshi Ohta
本文研究了内空间中缠绕在2-圈上的欧氏D-弦的有效拓扑场论。我们计算了一个合适的算子对应的真空期望值，该算子对应于束缚在D弦上的涡旋的化学势，并发现由于局域化，它约化为广义二维Yang-Mills理论的配分函数。我们认为，在适当的大N极限下，配分函数给出了四维N=2规范理论的多瞬子修正的巨正则系综。我们发现二维规范理论提供了四维N=2理论的瞬子配分函数，在伴随和基本表示的超多重态。我们还提出了一个配分函数，给出了四维N=2的规范理论的瞬子的贡献。本文从广义二维Yang-Mills理论的大N相变出发，讨论了Nekrasov的瞬子配分函数与Dijkgraaf-Vafa理论之间的关系。
We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vacuum expectation value of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the partition function gives a grand canonical ensemble of multi-instanton corrections for four-dimensional N=2 gauge theory in a suitable large N limit. We find two-dimensional gauge theories that provide the instanton partition function for four-dimensional N=2 theories with the hypermultiplets in the adjoint and fundamental representations. We also propose a partition function that gives the instanton contributions to four-dimensional N=2 quiver gauge theory. We discuss the relation between Nekrasov's instanton partition function and the Dijkgraaf-Vafa theory in terms of large N phase transitions of the generalized two-dimensional Yang-Mills theory.