slˆ(n)N WZW conformal blocks from SU(N) instanton partition functions on C2/Zn

Abstract

Generalizations of the AGT correspondence between 4D N=2 SU(2) supersymmetric gauge theory on C2 with Ω-deformation and 2D Liouville conformal field theory include a correspondence between 4D N=2 SU(N) supersymmetric gauge theories, N=2,3,…, on C2/Zn, n=2,3,…, with Ω-deformation and 2D conformal field theories with WN,npara (n-th parafermion WN) symmetry and slˆ(n)N symmetry. In this work, we trivialize the factor with WN,npara symmetry in the 4D SU(N) instanton partition functions on C2/Zn (by using specific choices of parameters and imposing specific conditions on the N-tuples of Young diagrams that label the states), and extract the 2D slˆ(n)N WZW conformal blocks, n=2,3,…, N=1,2,….