From SO/Sp instantons to W-algebra blocks

Christoph A. Keller; Jaewon Song; Lotte Hollands

From SO/Sp instantons to W-algebra blocks

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arxiv 1012.4468 v2 pith:JZVKKWPO submitted 2010-12-20 hep-th math.AG

Lotte Hollands , Christoph A. Keller , Jaewon Song This is my paper · ORCID

classification hep-thmath.AG

keywords instantoncorrespondencefunctionsblocksdifferentgaugemappingpartition

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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. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)-SO(4) half-bifundamental.

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The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.

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