English

Seiberg-Witten Theory and Random Partitions

High Energy Physics - Theory 2007-05-23 v2 Statistical Mechanics Mathematical Physics Algebraic Geometry math.MP Probability Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.hep-th/0306238,
  title  = {Seiberg-Witten Theory and Random Partitions},
  author = {Nikita Nekrasov and Andrei Okounkov},
  journal= {arXiv preprint arXiv:hep-th/0306238},
  year   = {2007}
}

Comments

90 pp. plain TeX, 15 pictures

R2 v1 2026-07-22T15:17:50.709Z