Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing

TL;DR

This paper explores how noncommutative gauge theories on the Groenewold-Moyal plane exhibit UV-IR mixing at one-loop level when involving nonabelian gauge fields, contrasting with the abelian case where mixing is absent.

Contribution

It demonstrates the presence of UV-IR mixing in nonabelian gauge theories on the GM plane, extending previous work that showed no mixing in scalar theories.

Findings

UV-IR mixing occurs in nonabelian gauge theories at one-loop level.

No UV-IR mixing is found in abelian gauge theories.

The study clarifies the role of gauge group structure in UV-IR mixing.

Abstract

In the absence of gauge fields, quantum field theories on the Groenewold-Moyal (GM) plane are invariant under a twisted action of the Poincare group if they are formulated following [1, 2, 3, 4, 5, 6]. In that formulation, such theories also have no UV-IR mixing [7]. Here we investigate UV-IR mixing in gauge theories with matter following the approach of [3, 4]. We prove that there is UV-IR mixing in the one-loop diagram of the S-matrix involving a coupling between gauge and matter fields on the GM plane, the gauge field being nonabelian. There is no UV-IR mixing if it is abelian.