Ontology type: schema:Chapter Open Access: True
2007-01-01
AUTHORSNikita A. Nekrasov , Andrei Okounkov
ABSTRACTWe study \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} = 2 $$\end{document} supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.These representations allow us to derive rigorously the Seiberg-Witten geometry, the curves, the differentials, and the prepotential.We study pure 525-03 = 2 theory, as well as the theory with matter hypermultiplets in the fundamental or adjoint representations, and the five-dimensional theory compactified on a circle. More... »
PAGES525-596
The Unity of Mathematics
ISBN
978-0-8176-4076-7
978-0-8176-4467-3
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DOIhttp://dx.doi.org/10.1007/0-8176-4467-9_15
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