No parity anomaly in massless QED3: a BPHZL approach

TL;DR

This paper demonstrates that the perceived parity anomaly in massless QED3 at 1-loop is actually a parity-odd counterterm, and not a true anomaly, using a regularization-independent BPHZL renormalization approach.

Contribution

The paper provides a scheme-independent proof that the 1-loop parity violation in massless QED3 is a counterterm, not a genuine anomaly, clarifying longstanding debates.

Findings

No true parity anomaly at 1-loop in massless QED3.

The Chern-Simons term arises from infrared subtractions, not an anomaly.

Parity-odd counterterm restores parity without anomaly.

Abstract

In this letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED_3 frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not will be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein-Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern-Simons term is generated at that order induced through the infrared subtractions -- which violate parity. We show then that, what is called parity anomaly, is in fact a parity-odd counterterm needed for restauring parity.