Scalar Higher Dimensional Theories in 1/N-expansion

This talk is based on the paper hep-th/0607177 where we demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in arbitrary high odd space-time dimension. The resulting effective coupling is dimensionless and is running in accordance with the usual RG equations. The corresponding beta function is calculated in the leading order and is nonpolynomial in effective coupling. It exhibits either UV asymptotically free or IR free behaviour depending on the dimension of space-time. In this talk we mainly discussed the problems concerning the Renormalization Group.