UV/IR mixing as a twisted Poincar\'{e} anomaly

TL;DR

This paper investigates how quantum effects break twisted Poincaré symmetry in noncommutative  field theory, revealing an anomaly at the 1-loop level despite classical invariance.

Contribution

It demonstrates that twisted Poincaré invariance is broken at 1-loop quantum level, highlighting the role of quantization methods in symmetry anomalies.

Findings

Twisted Poincaré invariance is lost at 1-loop level.

Quantum anomaly arises from quantization choices.

Classical symmetry does not guarantee quantum symmetry.

Abstract

We analyze symmetries of the 1-loop effective action of \phi^4 noncommutative field theory. It is shown, that despite the twisted Poincar\'{e} invariance of the classical noncommutative action, its 1-loop quantum counterpart lacks this invariance. Though Noether analysis of the model is somewhat obscure, it is still possible to interpret this symmetry breaking as a quantum anomaly due to inappropriate choice of the quantization method.