In this paper we review the properties of the 1/$N_f$ expansion in multidimensional theories. Contrary to the usual perturbative expansion it is renormalizable and contains only logarithmic divergencies. The price for it is the presence of ghost stat
es 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 $eq to eq$ scattering in $D=7,11,...$-dimensional world. We look also for the unification of the gauge couplings in multidimensional Standard Model and its SUSY extension which takes place at energies lower than in 4 dimensions.
We consider the regions of the MSSM parameter space where the top squarks become light and even may be the LSP. This happens when the triple scalar coupling A becomes very big compared to m_0. We show that in this case the requirement that the LSP is
neutral imposes noticeable constraint on the parameter space excluding low m_0 and m_{1/2} similar to constraint from the Higgs mass limit. In some cases these constraints overlap. This picture takes place in a wide region of tanbeta. In a narrow band close to the border line the stops are long-lived particles and decay into quarks and neutralino (chargino). The cross-section of their production at LHC via gluon fusion mechanism in this region may reach a few pb.
