Topological strings and Nekrasov's formulas
Topological strings and Nekrasov's formulas
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DOI：
10.1088/1126-6708/2003/12/006
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发表时间：
2003-10
影响因子：
5.4
通讯作者：
T. Eguchi;H. Kanno
中科院分区：
文献类型：
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作者：
T. Eguchi;H. Kanno
应用几何跃迁方法，利用chen - simons规范理论计算了局部F0上紧化的所有格拓扑闭弦振幅。我们发现我们的计算结果与Nekrasov最近为具有两个参数β和的= 2su(2)规范理论提出的公式完全一致。β与F0光纤的尺寸有关，对应于串耦合常数。因此Nekrasov公式编码了局部F0上拓扑弦幅值的全部信息，包括任意属全纯曲线的个数。通过取适当的极限β和/或→0，可以恢复四维Seiberg-Witten理论及其与外部重光子场的耦合。我们还计算了局部2nd del Pezzo曲面的拓扑弦振幅，并在向量表示的物质场中检验了与SU(2)规范理论的Nekrasov公式的一致性。
We apply the method of geometric transition and compute all genus topological closed string amplitudes compactified on local F0 by making use of the Chern-Simons gauge theory. We find an exact agreement of the results of our computation with the formula proposed recently by Nekrasov for = 2 SU(2) gauge theory with two parameters β and . β is related to the size of the fiber of F0 and corresponds to the string coupling constant. Thus Nekrasov's formula encodes all the information of topological string amplitudes on local F0 including the number of holomorphic curves at arbitrary genus. By taking suitable limits β and/or →0 one recovers the four-dimensional Seiberg-Witten theory and also its coupling to external graviphoton fields. We also compute topological string amplitude for the local 2nd del Pezzo surface and check the consistency with Nekrasov's formula of SU(2) gauge theory with a matter field in the vector representation.