Instantons and 2d superconformal field theory

A recently proposed correspondence between 4-dimensional SUSY SU( k ) gauge theories on and SU( k ) Toda-like theories with Z m parafermionic symmetry is used to construct four-point super Liouville conformal block, which corresponds to the particular case k = m = 2. The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on and algebras like . This conjecture is confirmed by checking the coincidence of number of fixed points on such instanton moduli space with given instanton number N and dimension of subspace degree N in the representation of such algebra.