2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51979We 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.90 pp. plain TeX, 15 picturesHigh Energy Physics - TheoryStatistical MechanicsMathematical PhysicsAlgebraic GeometryProbabilityExactly Solvable and Integrable Systemstext