Flavordynamics with Conformal Matter and Gauge Theories on Compact Hyperbolic Manifolds in Extra Dimensions

Abstract

We outline a toy model in which a unique mechanism may trigger a dynamical chain resulting in key low-energy regularities. The starting points are a negative cosmological term in the bulk and conformally invariant nongravity sector. These elements ensure compactification of the extra dimensional space on a compact hyperbolic manifold (with the negative and constant scalar curvature). The overall geometry is then M_4 x B_n. The negative curvature on B_n triggers the formation of the four-dimensional defect which provides in turn a dynamical localization of ordinary particles. It also leads, simultaneously, to a spontaneous breaking of gauge symmetry through a Higgs mechanism. Masses of the fermions, gauge bosons and scalars all derive from the curvature of the internal manifold such that the Higgs boson is generally heavier than the gauge bosons. The factorizable geometry M_4 x B_n and flatness of M_4 require fine-tuning.