N = 2 superconformal blocks and instanton partition functions

We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the N =2 superconformal algebra. Our construction uses two ingredients: (i) the relation between the representation theories of the N =2 superconformal algebra and the affine sl̂(2) algebra, extended to the level of the conformal blocks, and (ii) the relation between sl̂(2) conformal blocks and instanton partition functions in the 4d N =2 SU(2) gauge theory with a surface defect. By combining these two facts we derive combinatorial expressions for the N =2 superconformal blocks in the Gaiotto limit.