A Note on UV/IR for Noncommutative Complex Scalar Field

TL;DR

This paper investigates the renormalization properties of a noncommutative complex scalar field theory with specific quartic interactions, identifying conditions under which the model is one-loop renormalizable and free from IR divergences.

Contribution

It introduces a noncommutative analogue of a U(1)-invariant quartic interaction and analyzes its renormalizability, highlighting special cases with improved quantum behavior.

Findings

Model is nonrenormalizable for arbitrary couplings.

One-loop renormalizable when B=0 or A=B.

IR divergences absent at one-loop for B=0.

Abstract

Noncommutative quantum field theory of a complex scalar field is considered. There is a two-coupling noncommutative analogue of U(1)-invariant quartic interaction $(\phi^*\phi)^2$, namely $A\phi^*\star\phi\star\phi^*\star\phi+ B\phi^*\star\phi^*\star\phi\star\phi$. For arbitrary values of $A$ and $B$ the model is nonrenormalizable. However, it is one-loop renormalizable in two special cases: B=0 and $A=B$. Furthermore, in the case B=0 the model does not suffer from IR divergencies at least at one-loop insertions level.