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

Using higher-derivative gravitational action 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 four-dimensional space-time the resulting theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its 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 mass scale, (ii) phase transition at 1.76 x 10(16) GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 1.76 x 10(16) GeV should be fractal.