Effective Field Theory of a Locally Noncommutative Space-Time and Extra Dimensions

TL;DR

This paper develops an effective field theory framework for noncommutative space-times and extra dimensions, showing the absence of UV/IR mixing and exploring implications for UV completion and compactification scales.

Contribution

It derives a two-loop effective action for noncommutative scalar theories that are free of UV/IR mixing and analyzes the role of positivity constraints and extra dimensions.

Findings

Effective theories are free of UV/IR mixing phenomena.

Positivity constraints relate to UV completion of the theory.

Noncommutative extra dimensions can avoid UV/IR mixing if compactification scale is below noncommutativity scale.

Abstract

We assume that the noncommutativity starts to be visible continuously from a scale $\Lambda_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $\phi^{4}$ and $\phi^{3}$ theories from a Wilsonian point of view. We show that these effective theories are free of UV/IR mixing phenomena. We also investigate the positivity constraint on coefficients of higher dimension operators present in the effective theory. This constraint makes the low energy theory to be UV completion of a full theory. Finally, we discuss noncommutativity and extra dimensions. In our effective theories formulated on noncommutative extra dimensions, if the campactification scale $\Lambda_{c}$ is less than the scale $\Lambda_{NC}$, the theory will not suffer from UV/IR mixing.