RENORMALIZATION-GROUP AND SPONTANEOUS COMPACTIFICATION OF A HIGHER-DIMENSIONAL SCALAR FIELD-THEORY IN CURVED SPACETIME

The renormalization group (RG) is used to study the asymptotically fre e phi(6)(3) theory in curved spacetime. Several forms of the RG equati ons for the effective potential are formulated. By solving these equat ions we obtain the one-loop effective potential as well as its explici t forms in the case of strong gravitational fields and strong scalar f ields. Using zeta-function techniques, the one-loop vacuum energy and corresponding RG-improved vacuum energy are found for the Kaluza-Klein backgrounds R(4)XS(1)XS(1) and R(4)XS(2). They are given in terms of exponentially convergent series, appropriate for numerical calculation s. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification ca n be qualitatively different when the RG-improved energy is used.