"Surface operators, separation of variables and conformal field theory"

We revisit relations between instanton partition functions for N=2 SUSY gauge theories of class S in the presence of surface operators, and conformal field theory. For surface operators of codimension four one expects to get Liouville (Toda) conformal blocks with degenerate fields, in the codimension two case conformal blocks of noncompact WZNW models. The two types of conformal blocks are sometimes related by an integral transformation. We argue that these relations between conformal blocks imply an IR duality between the two types of surface operators.

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