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

E. Elizalde·R. Kantowski·S. D. Odintsov
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Abstract

The renormalization group (RG) is used to study the asymptotically free $ϕ_6^3$-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.

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E. Elizalde, R. Kantowski, S. D. Odintsov. 1996-01-19. The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime. https://doi.org/10.1103/physrevd.54.6372

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