From SO/Sp instantons to Walgebra blocks
Abstract
We study instanton partition functions for mathcal{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 nontrivial 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 AGTtype correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying mathcal{W}left( {2,2} right) 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) halfbifundamental.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2011
 DOI:
 10.1007/JHEP03(2011)053
 arXiv:
 arXiv:1012.4468
 Bibcode:
 2011JHEP...03..053H
 Keywords:

 Supersymmetric gauge theory;
 Nonperturbative Effects;
 Conformal and W Symmetry;
 MTheory;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 83 pages, 29 figures