Seiberg-Witten Theory and Random Partitions

  • Nikita A. Nekrasov
  • Andrei Okounkov
Part of the Progress in Mathematics book series (PM, volume 244)


We study \( \mathcal{N} = 2 \) 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.


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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Nikita A. Nekrasov
    • 1
  • Andrei Okounkov
    • 2
  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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