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We study the regular surface defect in the Omega-deformed four-dimensionalsupersymmetric gauge theory with gauge group SU(N) with 2N hypermultiplets infundamental representation. We prove its vacuum expectation value obeys theKnizhnik-Zamolodchikov equation for the 4-point conformal block of currentalgebra of a two-dimensional conformal field theory. The level and the vertexoperators are determined by the parameters of the Omega-background and themasses of the hypermultiplets; the cross-ratio of the 4 points is determined bythe complexified gauge coupling. We clarify that in a somewhat subtle way thebranching rule is parametrized by the Coulomb moduli. This is an example of theBPS/CFT relation.

Surface defects in gauge theory and KZ equation