TOPOLOGICAL ORIGIN OF THE COUPLING CONSTANTS HIERARCHY IN KALUZA–KLEIN APPROACH

Abstract

We consider an Abelian BF-model in the frame of ten-dimensional Kaluza–Klein approach on the space T2×X×M, where X belongs to the class of four-dimension decorated plumbed cobordisms (dp-cobordisms) and M is an An-1-singularity resolution manifold homeomorphic to a compactified ALE space. These four-dimensional manifolds with boundaries possess nontrivial cohomology properties that lead to a specific generalization of the Dirac quantization conditions and enables us to express classical partition functions in terms of 4-form fluxes through the direct product of nontrivial 2-cycles associated with the manifolds X and M. The intersection matrices of these manifolds play the role of coupling constants for the fluxes. We build several examples of dp-cobordisms containing in their intersection matrices the hierarchy of dimensionless low-energy coupling constants of interactions which are available in the real universe. We also consider the phenomenon of "running coupling constants," in particular the cosmological constant evolution induced by the topology changes of internal space X.