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Following a recent paper by Alday and Tachikawa, we compute the instantonpartition function in the presence of the surface operator by the localizationformula on the moduli space. For SU(2) theories we find an exact agreement withCFT correlation functions with a degenerate operator insertion, which enablesus to work out the decoupling limit of the superconformal theory with fourflavors to asymptotically free theories at the level of differential equationsfor CFT correlation functions (irregular conformal blocks). We also argue thatthe K theory (or five dimensional) lift of these computations gives opentopological string amplitudes on local Hirzebruch surface and its blow ups,which is regarded as a geometric engineering of the surface operator. Bycomputing the amplitudes in both A and B models we collect convincing evidencesof the agreement of the instanton partition function with surface operator andthe partition function of open topological string.

Localization with a surface operator, irregular conformal blocks and open topological string