No radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences

The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field b_\m -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.Comment: In honor of Prof. Manfred Schweda (1939-2017). Work presented at the XXXVIII National Meeting on Particle Physics and Fields, September 18-22, 2017 - Passa Quatro - Minas Gerais - Brazil. Reference [46] correcte

An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3

A rigorous algebraic proof of the full finiteness in all orders of perturbation theory is given for the Yang-Mills-Chern-Simons theory in a general three-dimensional Riemannian manifold. We show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all loop orders, which yields the vanishing of the beta-functions associated to the topological mass and gauge coupling constant as well as the anomalous dimensions of the fields.Comment: 5 pages, revte

Algebraic Renormalization of Parity-Preserving QED_3 Coupled to Scalar Matter II: Broken Case

In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED_3 coupled to scalar matter in the broken regime, where the scalar assumes a finite vacuum expectation value, $= v$. The model shows to be stable under radiative corrections and anomaly free.Comment: 9 pages, latex, no figure

On the strict positivity and the spectrum of the two-dimensional Brown-Ravenhall operator with an attractive potential of the Bessel-Macdonald type

The Brown-Ravenhall operator was initially proposed as an alternative to describe the fermion-fermion interaction via Coulomb potential and subject to relativity. This operator is defined in terms of the associated Dirac operator and the projection onto the positive spectral subspace of the free Dirac operator. In this paper, we propose to analyze a modified version of the Brown-Ravenhall operator in two-dimensions. More specifically, we consider the Brown-Ravenhall operator with an attractive potential given by a Bessel-Macdonald function (also known as $K_0$-potential) using the Foldy-Wouthuysen unitary transformation. The $K_0$-potential is derived of the parity-preserving ${\rm QED}_3$ model as a framework for evaluation of the fermion-fermion interaction potential. We prove that the two-dimensional Brown-Ravenhall operator with $K_0$-potential is bounded from below when the coupling constant is below a specified critical value (a property also referred to as stability). As by product, it is shown that the operator is in fact positive. We also investigate the location and nature of the spectrum of the Brown-Ravenhall operator with $K_0$-potential.Comment: 15 page

N=1 Chern-Simons theories, orientifolds and Spin(7) cones

We construct three dimensional N=1 Chern-Simons theories living on M2 branes probing Spin(7) cones. We consider Spin(7) manifolds obtained as quotients of Calabi-Yau four-folds by an anti-holomorphic involution, following a construction by Joyce. The corresponding Chern-Simons theories can be obtained from N=2 theories by an orientifolding procedure. These theories are holographically dual to M theory solutions AdS_4 \times H, where the weak G_2 manifold H is the base of the Spin(7) cone.Comment: 26 pages, 3 figures, reference added