Seiberg-Witten Theory and Random Partitions
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2003
- DOI:
- 10.48550/arXiv.hep-th/0306238
- arXiv:
- arXiv:hep-th/0306238
- Bibcode:
- 2003hep.th....6238N
- Keywords:
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- High Energy Physics - Theory;
- Condensed Matter - Statistical Mechanics;
- Mathematical Physics;
- Mathematics - Algebraic Geometry;
- Mathematics - Mathematical Physics;
- Mathematics - Probability;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 90 pp. plain TeX, 15 pictures