Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-08-03
Physics
High Energy Physics
High Energy Physics - Theory
73 pages, 8 figures. v2: minor changes in section 6 and Appendix A, typos corrected and references added. v3: sections 1--3 re
Scientific paper
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.
Awata Hidetoshi
Fuji Hiroyuki
Kanno Hiroaki
Manabe Masahide
Yamada Yasuhiko
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