Affine sl(N) conformal blocks from N=2 SU(N) gauge theories

Recently Alday and Tachikawa [1] proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N = 2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N) symmetry and instanton partition functions in conformal N = 2 SU(N) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N = 2 SU(N) theories.