On the absence of parity anomaly and the finiteness of massless QED₃

Full text: In this work we call into question some unclear points concerning the perturbatively parity breakdown at 1-loop for the massless QED₃ frequently claimed in the literature. There are some claims in the literature that Pauli- Villars regularization must be used because it does not break gauge invariance, contrary to the dimensional regularization case, that is not true in the light of perturbation theory for massless QED₃. Moreover, Pauli- Villars breaks parity, dimensional regularization does not, both preserve gauge invariance, which of them is more suitable in the quantization of the massless QED₃? Such a question makes no sense if both schemes are properly used. Fortuitous breaking of gauge symmetry happens when there is no invariant regularization scheme available, however, the Quantum Action Principle guarantees that they can be completely eliminated, when gauge anomaly is absent, by the introduction of noninvariant local counterterms at each perturbative order. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. We show algebraically, by adopting the Lowenstein-Zimmermann subtraction scheme, that the massless QED3 is perturbatively finite and parity anomaly free. We conclude from the Quantum Action Principle to the absence of noninvariant counterterms at the level of the Slavnov-Taylor identity, avoiding in this way a possible parity anomaly that could be induced by parity-odd noninvariant counterterms. The 1-loop parity-odd contribution to the vacuum-polarization tensor is also 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 IR subtractions (which breaks parity), therefore, what is called 'parity anomaly' is in fact a parity-odd counterterm. (author)