Phenomenology of the 1/Nf expansion for field theories in extra dimensions

In this paper we review the properties of the 1/N f expansion in multi-dimensional theories. Contrary to the usual perturbative expansion it is renormalizable and contains only logarithmic divergencies. The price for it is the presence of ghost states, which, however, in certain cases do not contribute to physical amplitudes. In this case the theory is unitary and one can calculate the cross-sections. As an example we consider the differential cross-section of elastic eq→eq scattering in a D=7,11,...-dimensional world. We look also for the unification of the gauge couplings in the multi-dimensional standard model and its SUSY extension, which occurs at energies lower than in 4 dimensions.