TY - CHAP

T1 - Seiberg-Witten theory and random partitions

AU - Nekrasov, Nikita A.

AU - Okounkov, Andrei

PY - 2006

Y1 - 2006

N2 - We study 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.

AB - We study 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.

UR - http://www.scopus.com/inward/record.url?scp=84996426477&partnerID=8YFLogxK

U2 - 10.1007/0-8176-4467-9_15

DO - 10.1007/0-8176-4467-9_15

M3 - Chapter

AN - SCOPUS:84996426477

T3 - Progress in Mathematics

SP - 525

EP - 596

BT - Progress in Mathematics

PB - Springer Basel

ER -