Abstract
Generalizations of the AGT correspondence between 4D N=2SU(2) supersymmetric gauge theory on C2 with Ω-deformation and 2D Liouville conformal field theory include a correspondence between 4D N=2SU(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,….
Highlights
We show that the integrable sl(n)N WZW conformal blocks can be extracted from the instanton partition functions by an appropriate choice of the parameters and imposing the appropriate Burge conditions
In Appendix A, we summarize the notation of Lie algebras that is used in this paper, in Appendix B, we review some AGT correspondences to confirm our conventions, and in Appendix C, we recall a class of integrable sl(n)N WZW 4-point conformal blocks computed in [28], which we compare in Section 7 with our results
We review how the moduli space of U(N ) instantons on C2/Zn with Ω-deformation is characterized by coloured Young diagrams, and define the generating functions of the coloured Young diagrams and the instanton partition functions
Summary
On imposing the Burge conditions (4.3) on the generating functions of coloured Young diagrams 9 and instanton partition functions, the sl(n)N WZW characters and conformal blocks emerge. SN−1] by (5.1) and (5.2), and define the SU(N ) t-refined Burge-reduced generating function of coloured Young diagrams, by subtracting the Heisenberg factor H whose character is χH(q) = (q; q)−∞1 in (2.11), (5.21)
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