The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime

Abstract

The renormalization group (RG) is used to study the asymptotically free ${\varphi }_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop effective potential as well as its explicit forms in the case of strong gravitational fields and strong scalar fields. Using zeta function techniques, the one-loop and corresponding RG improved vacuum energies are found for the Kaluza-Klein backgrounds $R^4\times S^1\times S^1$ and $R^4\times S^2$. They are given in terms of exponentially convergent series, appropriate for numerical calculations. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification can be qualitatively different when the RG improved energy is used.

LaTeX, 15 pages, 4 figures

References in corpus (5)

• The effective potential and the renormalisation group
• Are Nonrenormalizable Gauge Theories Renormalizable?
• Renormalization-group improved effective potential for gauge theories in curved spacetime
• Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime
• Gauge Independent Trace Anomaly for Gravitons

Cited by in corpus (1)

• Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity