期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 8, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP08(2012)046
关键词
Matrix Models; Duality in Gauge Field Theories
资金
- J. C. Bose fellowship of the Department of Science and Technology, India
- [11-RD-HRI-5.02-0304]
- National Research Foundation of Korea [2010-0008084] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
We study the beta-ensemble that represents conformal blocks of Liouville theory on the sphere. This quantity is related through AGT conjecture to the Nekrasov instanton partition function of 4d N = 2 SU(2) gauge theory with four flavors. We focus on the large N limit, equivalent to the Nekrasov-Shatashvili limit where one of the Omega-background deformation parameters is vanishing. A quantized Seiberg-Witten differential form is defined perturbatively in h as the singular part of the beta-ensemble resolvent. Using the Dyson collective field action, we show that the free energy obeys the Seiberg-Witten relations. As suggested by Mironov and Morozov, the quantized differential form can be obtained from the classical one by the action of a differential operator in the hypermultiplet masses and the Coulomb branch modulus.
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