From SO/Sp instantons to W-algebra blocks

Understand

We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories.

• We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes.
• Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings.
• We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2,2)-algebra symmetry.