The ABCDEFG of instantons and W-algebras

Creators: Keller, Christoph A.; Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji

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Abstract

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N = 2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.

Additional Information

© 2012 SISSA. Published for SISSA by Springer. Received: February 11, 2012. Accepted: February 16, 2012. Published: March 15, 2012. The authors thank the initial wavefunction of the universe, which arranged so that NM and JS visited IPMU on the same week, without which this paper would not have been written. They also thank Kris Thielemans, who provided them the Mathematica package OPEdefs.m, without which the calculation was not possible. They also thank IPMU mathematicians Alexey Bondal and Scott Carnahan for their help in simplifying the Hilbert series into the closed form. They also thank Amihay Hanany, Lotte Hollands and Michael Kay for useful discussions. They also thank Nick Dorey for his advice on the correct usage of the English definite article the used in the title of the paper. NM and JS also thank the hospitality of IPMU during their visit. The work of CAK is supported by a John A. McCone Postdoctoral Fellowship. The work of NM is supported by a research grant of the Max Planck Society. This work is in addition supported in part by the DOE grant DE-FG03-92-ER40701. The work of YT is supported in part by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan through the Institute for the Physics and Mathematics of the Universe, the University of Tokyo.

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