Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String
Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String
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DOI：
10.4310/atmp.2012.v16.n3.a1
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发表时间：
2010-08
影响因子：
1.5
通讯作者：
H. Awata;H. Fuji;H. Kanno;Masahide Manabe;Y. Yamada
中科院分区：
文献类型：
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作者：
H. Awata;H. Fuji;H. Kanno;Masahide Manabe;Y. Yamada
根据Alday和Tachikawa最近的一篇论文，我们通过模空间上的局部化公式计算了表面算子存在下的瞬子配分函数。对于SU（2）理论，我们发现与带有退化算子插入的CFT相关函数完全一致，这使我们能够在CFT相关函数的微分方程水平上计算出具有四种风味的超共形理论与渐进自由理论的解耦极限（不规则共形块）。我们还认为，这些计算的K理论（或五维）提升给出了局部Hirzebruch曲面上的开拓扑弦振幅及其爆破，这被视为曲面算子的几何工程。通过计算A和B模型的振幅，我们得到了瞬子配分函数与表面算符和开拓扑弦配分函数一致的令人信服的证据。
Following a recent paper by Alday and Tachikawa, we compute the instanton partition function in the presence of the surface operator by the localization formula on the moduli space. For SU(2) theories we find an exact agreement with CFT correlation functions with a degenerate operator insertion, which enables us to work out the decoupling limit of the superconformal theory with four flavors to asymptotically free theories at the level of differential equations for CFT correlation functions (irregular conformal blocks). We also argue that the K theory (or five dimensional) lift of these computations gives open topological string amplitudes on local Hirzebruch surface and its blow ups, which is regarded as a geometric engineering of the surface operator. By computing the amplitudes in both A and B models we collect convincing evidences of the agreement of the instanton partition function with surface operator and the partition function of open topological string.