Riccion from higher-dimensional space-time and one-loop renormalization

Using higher-dimensional gravity in (4+D)-dimensional space-time, Lagrangian density of riccion is obtained with the quartic self-interacting potential. It is found that after compactification to 4-dimensional space-time the resulting theory is one-loop multiplicatively renormalizable. Renormalization group equations are solved and their solutions yield many interesting results such as (i) dependence of extra dimensions on the energy mass scale showing that these dimensions increase with the increasing energy mass scale such that D = 6 at extremely high energy; (ii) phase transition at 2.82 x 1016GeV; and (iii) dependence of gravitational as well as other coupling constants on energy scale. Results also suggest that space-time above 2.82 x 1016GeV should be fractal. (author)