Gravitational quantum foam and supersymmetric gauge theories Original Research Article

We study Kähler gravity on local image geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi–Yau threefold, that is a image singularity fibred over image. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional image supersymmetric image Yang–Mills. These quanta are labelled by lattice points in a certain convex polyhedron on image. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown to consist of N unit cubes of plane partitions.