SeibergWitten Theory and Random Partitions
Abstract
We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omegabackground. The partition function of the theory in the Omegabackground 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 SeibergWitten 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:

arXiv eprints
 Pub Date:
 June 2003
 arXiv:
 arXiv:hepth/0306238
 Bibcode:
 2003hep.th....6238N
 Keywords:

 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
 EPrint:
 90 pp. plain TeX, 15 pictures