Seiberg-Witten Theory and Random Partitions

Nikita Nekrasov; Andrei Okounkov

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arXiv · hep-th/0306238

Seiberg-Witten Theory and Random Partitions

Nikita Nekrasov·Andrei Okounkov

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Abstract

We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omega-background. The partition function of the theory in the Omega-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, a free fermion correlator. These representations allow to derive rigorously the Seiberg-Witten geometry, the curves, the differentials, and the prepotential. We study pure N=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.

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hep-th cond-mat.stat-mech math-ph math.AG math.MP math.PR nlin.SI

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Nikita Nekrasov, Andrei Okounkov. 2003-06-25. Seiberg-Witten Theory and Random Partitions. https://arxiv.org/abs/hep-th/0306238

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