Seiberg-Witten theory and random partitions

Nikita A. Nekrasov, Andrei Okounkov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

405 Citations (Scopus)


We study N = 2 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.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Number of pages72
Publication statusPublished - 2006
Externally publishedYes

Publication series

NameProgress in Mathematics
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X


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