Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions

Details Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions

2006-04-20

arxiv.org/abs/hep-th/0604141v2

Prog.Theor.Phys.116:1131-1157,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 11 figures; v2 typos corrected

Scientific paper

10.1143/PTP.116.1131

We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov's partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model we reproduce the polyhedron which characterizes the Hilbert space.

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