Summary
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.
ITEP Moscow 117259 Russia (on leave of absence)
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Nekrasov, N.A., Okounkov, A. (2006). Seiberg-Witten Theory and Random Partitions. In: Etingof, P., Retakh, V., Singer, I.M. (eds) The Unity of Mathematics. Progress in Mathematics, vol 244. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4467-9_15
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