Effective action and spontaneous compactification in Kaluza-Klein quantum R2-gravity

The one-loop effective action for some variants of d-dimensional quantum R2-gravity and for the special model of multidimensional gravity on the background M4 . Td-x, where M4 is the Minkowski space, Td-4 is the (d-4)-dimensional torus, is obtained. It is shown that the effective action of the R2-gravity without the cosmological and Einstein terms leads to instability of classical compactification. It is shown by numerical calculations that the effective action of five-dimensional R2-gravity with the cosmological term admits self-consistent spontaneous compactification. The one-loop effective action for the five-dimensional Einstein gravity with antisymmetric torsion on the background M4 . S1 is also found. (orig.)