Parity anomalies in gauge theories in 2 + 1 dimensions

Spontaneous chiral-symmetry breaking in three-dimensional QED with a Chern-Simons term

“…Without the CS term in the Lagrangian, we have no explicit parity breaking terms, and the full fermion propagator will also be parity even: there will be no spontaneous breaking of parity [10][11][12][13][14][15][16]. That means that we only have to deal with one set of two coupled integral equations for A(p) and B(p)…”

“…A field-theoretic realization of such an anyonic model consists of fermions interacting with an abelian statistical gauge field whose dynamics is governed by a CS term. In contrast to the chiral symmetry, it is known that the dynamical breakdown of parity does not occur in QED3 [10][11][12][13][14][15][16].…”

Induced Chern-Simons term in lattice QCD at finite temperature

“…One normally encounters the same conclusion as to P -or CP -odd effects independently of the method of determinant analysis. They result from the Chern-Simons action [22], [23] though the coefficients of the Chern-Simons term turn out to be different for various regularization schemes [24].…”

Ultraviolet and infrared perturbative finiteness of masslessQED3

“…In spite of not being a topological field theory, the massless QED 3 is also perturbatively finite, exhibiting quite interesting and subtle properties as superrenormalizability, parity invariance and the presence of infrared divergences. The issue of "how superrenormalizable interactions cure their infrared divergences" has been analyzed in [3], and a possible parity breaking at the quantum level, in the literature called parity anomaly, has been discarded [4][5][6].The algebraic proof we are presenting in this letter on the ultraviolet and infrared finiteness, and absence of parity and infrared anomaly, in the massless QED 3 , is based on general theorems of perturbative quantum field theory [7][8][9][10], where the Lowenstein-Zimmermann subtraction scheme is adopted. Here we summarize the main results skipping the intermediate steps of the LowensteinZimmermann subtraction scheme in the framework of BPHZL renormalization method [10].…”

“…In spite of not being a topological field theory, the massless QED 3 is also perturbatively finite, exhibiting quite interesting and subtle properties as superrenormalizability, parity invariance and the presence of infrared divergences. The issue of "how superrenormalizable interactions cure their infrared divergences" has been analyzed in [3], and a possible parity breaking at the quantum level, in the literature called parity anomaly, has been discarded [4][5][6].…”