2-LOOP EFFECTIVE POTENTIAL IN QUANTUM-GRAVITY

The two-loop effective potential in multidimensional Einstein gravity with a cosmological constant is calculated on the background M(N) x T(k), where M(N) is a Minkowski space and T(k) is the k-dimensional torus. A detailed analysis is given of the case of five-dimensional gravity, for which the asymptotic forms of the two-loop effective potential are calculated and it is shown that the quantum spontaneous compactification is unstable.