From SO/Sp instantons to W-algebra blocks

Details From SO/Sp instantons to W-algebra blocks From SO/Sp instantons to W-algebra blocks

2010-12-20

arxiv.org/abs/1012.4468v2

JHEP 1103:053,2011

Physics

High Energy Physics

High Energy Physics - Theory

83 pages, 29 figures; minor changes

Scientific paper

10.1007/JHEP03(2011)053

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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