抄録
We derive the relation between the Hilbert space of certain geometries with the Bohr-Sommerfeld quantization and perturbative prepotentials for supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matter fields and one massive adjoint matter field. The gauge theory with one adjoint matter field possesses 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 a polyhedron that characterizes the Hilbert space.
