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June 2012 Localization with a surface operator, irregular conformal blocks and open topological string
Hidetoshi Awata, Hiroyuki Fuji, Hiroaki Kanno, Masahide Manabe, Yasuhiko Yamada
Adv. Theor. Math. Phys. 16(3): 725-804 (June 2012).


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 conformal field theory (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.


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Hidetoshi Awata. Hiroyuki Fuji. Hiroaki Kanno. Masahide Manabe. Yasuhiko Yamada. "Localization with a surface operator, irregular conformal blocks and open topological string." Adv. Theor. Math. Phys. 16 (3) 725 - 804, June 2012.


Published: June 2012
First available in Project Euclid: 20 March 2013

zbMATH: 1273.81178
MathSciNet: MR3024274

Rights: Copyright © 2012 International Press of Boston


Vol.16 • No. 3 • June 2012
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