Asymptotic Freedom in Noninteger Dimensional Spaces

This paper shows that as the dimensionality of a noninteger dimensional falls below 2, the potential becomes constant irrespective of separation between objects and the force between them disappears, which represents a new paradigm of asymptotic freedom. Since asymptotic freedom is at the basis of many applications such as those of strange metals, unconventional superconductors, and fractional quantum Hall states, the new paradigm presented here can potentially have new and unexpected applications. It also is of relevance to the study of anomalous mechanical effects that are important in metamaterials.