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Published March 10, 2011 | public
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From SO/Sp instantons to W-algebra blocks

Hollands, Lotte
Keller, Christoph A. ORCID icon
Song, Jaewon ORCID icon
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Abstract

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.

Additional Information

© 2011 Springer. Received: January 11, 2011; accepted: March 1, 2011; published: March 10, 2011. It is a pleasure to thank Matthias Gaberdiel, Sergei Gukov, Daniel Jafferis, Marcos Mariño, Yu Nakayama, Hirosi Ooguri, Vasily Pestun. We would like to especially thank Fernando Alday and Yuji Tachikawa for many useful suggestions, helpful explanations and enlightening discussions, Fernando Alday for helping us to find some of the exact series in section 2 and Yuji Tachikawa for carefully reading the manuscript. The work of LH is supported by an NWO Rubicon grant and by NSF grant PHY- 0757647. The work of CAK is supported by a John A. McCone Postdoctoral Fellowship. The work of JS is supported in part by a Samsung Scholarship. This work is in addition supported in part by the DOE grant DE-FG03-92-ER40701. LH thanks the Mathematical Institute at the University of Oxford, the University of Amsterdam, the Aspen Center for Physics and the KITP at Santa Barbara for kind hospitality during the process of this project. LH and JS as well thank the organizers of the Eighth Simons Workshop in Mathematics and Physics at the Stony Brook University. JS thanks the hospitality of Korea Institute for Advanced Study and CAK thanks the Erwin Schrödinger Institute in Vienna for hospitality.

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