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We consider the problem of computing N=2 superconformal block functions. Weargue that the Kazama-Suzuki coset realization of N=2 superconformal algebra interms of the affine sl(2) algebra provides relations between N=2 and affinesl(2) conformal blocks. We show that for N=2 chiral fields the correspondingsl(2) construction of the conformal blocks is based on the ordinary highestweight representation. We use an AGT-type correspondence to relate thefour-point sl(2) conformal block with Nekrasov's instanton partition functionsof a four-dimensional N=2 SU(2) gauge theory in the presence of a surfaceoperator. Since the previous relation proposed by Alday and Tachikawa requiressome special modification of the conformal block function, we revisit thisproblem and find direct correspondence for the four-point conformal block. Wethus find an explicit representation for the affine sl(2) four-point conformalblock and hence obtain an explicit combinatorial representation for the N=2chiral four-point conformal block.

Conformal blocks of Chiral fields in N=2 SUSY CFT and Affine Laumon Spaces