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 φ3 theory in six-dimensional spacetime, if to compactify two spatial dimensions on a 2D closed manifold. The result can be considered as an effective 4D theory of infinitely many KKtype scalar fields with triple interactions. The effective dimensional coupling constant 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. Freedom is not worth having if it does not include the freedom to make mistakes. Mahatma Gandhi.