Curing the UV/IR mixing for field theories with translation-invariant $\star$ products

TL;DR

This paper demonstrates that quantum corrections can be used to modify noncommutative field theories with translation-invariant products, successfully curing the UV/IR mixing problem through explicit loop calculations.

Contribution

It extends the method of using quantum corrections to cure UV/IR mixing from Moyal space to more general translation-invariant products, with explicit calculations.

Findings

Quantum corrections modify the noncommutative action.

The UV/IR mixing is cured in the new framework.

Explicit loop calculations support the approach.

Abstract

The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation- invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness, we compute the form of the new action in the matrix base for the Wick-Voros product.