No parity anomaly in massless QED3: a BPHZL approach

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.

4 pages, no figures, to appear in Physics Letters B

References in corpus (4)

• Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory
• What's Wrong with Pauli-Villars Regularization in $QE{D}_3$ ?
• BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory
• Induced Parity Violation in Odd Dimensions

Cited by in corpus (8)

• On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics
• The quantum scale invariance in graphene-like quantum electrodynamics
• Quantum parity conservation in planar quantum electrodynamics
• The parity-preserving massive QED3: vanishing beta-function and no parity anomaly
• Non-Perturbative Dynamics, Pair Condensation, Confinement and Dynamical Masses in Massless QED2+1
• Parity anomaly with impurities and the Pauli--Villars subtraction
• On the ultraviolet finiteness of parity-preserving $U(1)\times U(1)$ massive QED${}_3$
• The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond