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.

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