Instantons and 2d superconformal field theory

A recently proposed correspondence between 4-dimensional N = 2 SUSY SU(k) gauge theories on R4/Zm and SU(k) Toda-like theories with Zm parafermionic symmetry is used to construct four-point N = 1 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 R4/Z2 and algebras like bgl(2)2 × NSR. 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.