Can effective four-dimensional scalar theory be asymptotically free in a spacetime with extra dimensions?

Abstract

We trace what happens with asymptotically free behavior of the running coupling in ${\varphi }^3$ theory in six-dimensional space-time if to compactify two spatial dimensions on a 2D closed manifold. The result can be considered as an effective 4D theory of infinitely many KK-type scalar fields with triple interactions. The effective \emph{dimensional} coupling inherits running to zero at high mass scales in a modified form depending on the size of the compact manifold. Some physical implications are discussed.

25 pages, 2 figures. Typos in two formulas are correted

References in corpus (7)

• Ten years of the Analytic Perturbation Theory in QCD
• Critical exponents from five-loop scalar theory renormalization near six-dimensions
• Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics
• Decoupling of Heavy Kaluza-Klein Modes In Models With Five-Dimensional Scalar Fields
• Notes on sphere-based universal extra dimensions
• A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
• One-loop order effects from one universal extra dimension on $\lambda {\varphi }^4$ theory