Probing the Nielsen identities

We present some comments concerning the validity of the Nielsen identities for renormalizable theories quantized in general linear covariant gauges in a context of compact gauge Lie groups.Comment: 5 pages, Revtex, eq.(8) rewritten as properly suggested by the referee, one reference updated, final version to appear in Phys.Lett.

Twisted N=4 SUSY Algebra in Topological Models of Schwarz Type

We reinvestigate the twisted N=4 supersymmetry present in Schwarz type topological field models. We show that Chern-Simons theory in three dimensions can be untwisted to a kind of sigma-model with reversed statistics only in the free case. By dimensional reduction we define then the two-dimensional BF-model. We establish an analog result concerning the untwisting. As a consequence of the definition through dimensional reduction we find new fermionic scalar symmetries that have been overlooked so far in the literature.Comment: 12 pages, no figure, Late

Superpropagators for explicitly broken 3D-supersymmetric theories

A systematic algorithm to derive superpropagators in the case of either explicitly or spontaneously broken supersymmetric three-dimensional theories is presented. We discuss how the explicit breaking terms that are introduced at tree-level induce 1-loop radiative corrections to the effective action. We also point out that the renormalisation effects and the breaking-inducing-breaking mechanism become more immediate whenever we adopt the shifted superpropagators discussed in this letter.Comment: 6 pages, LaTex, references added. To appear in Phys.Lett.

Ghost free dual vector theories in 2+1 dimensions

We explore here the issue of duality versus spectrum equivalence in abelian vector theories in 2+1 dimensions. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show that the latter contains a ghost mode contrary to the original GSD model. On the other hand, the same embedding procedure can be applied to $N_f$ fermions minimally coupled to the self-dual model. The dual theory corresponds to $N_f$ fermions with an extra Thirring term coupled to the gauge field via a Pauli-like term. By integrating over the fermions at $N_f\to\infty$ in both matter coupled theories we obtain effective quadratic theories for the corresponding vector fields. On one hand, we have a nonlocal type of the GSD model. On the other hand, we have a nonlocal form of the MCS theory. It turns out that both theories have the same spectrum and are ghost free. By figuring out why we do not have ghosts in this case we are able to suggest a new master action which takes us from the local GSD to a nonlocal MCS model with the same spectrum of the original GSD model and ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.Comment: 15 pages, 1 figur

On the trace identity in a model with broken symmetry

Considering the simple chiral fermion meson model when the chiral symmetry is explicitly broken, we show the validity of a trace identity -- to all orders of perturbation theory -- playing the role of a Callan-Symanzik equation and which allows us to identify directly the breaking of dilatations with the trace of the energy-momentum tensor. More precisely, by coupling the quantum field theory considered to a classical curved space background, represented by the non-propagating external vielbein field, we can express the conservation of the energy-momentum tensor through the Ward identity which characterizes the invariance of the theory under the diffeomorphisms. Our ``Callan-Symanzik equation'' then is the anomalous Ward identity for the trace of the energy-momentum tensor, the so-called ``trace identity''.Comment: 11 pages, Revtex file, final version to appear in Phys.Rev.

Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal Chern-Simons-Matter Theory

We introduce an anti-symmetric metric into a 3-algebra and call it a symplectic 3-algebra. The N=6, Sp(2N) X U(1) superconformal Chern-Simons-matter theory with SU(4) R-symmetry in three dimensions is constructed by specifying the 3-brackets in a symplectic 3-algebra. We also demonstrate that the N=6, U(M) X U(N) theory can be recast into this symplectic 3-algebraic framework.Comment: 17 pages, version accepted for publication in EPJC. Section 4 added, showing that the N=6, U(M) X U(N) theory can be recast into the symplectic 3-algebraic framework. Previous Appendix A delete

N=1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time

In this letter, we present the Parkes-Siegel formulation for the massive Abelian $N$$=$$1$ super-{\QED} coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from ($2$$+$$2$) to ($1$$+$$2$) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ coupled to a Chern-Simons term naturally comes out.Comment: 7 pages, latex, no figure

Lorentz-invariant CPT violation

A Lorentz-invariant CPT violation, which may be termed as long-distance CPT violation in contrast to the familiar short-distance CPT violation, has been recently proposed. This scheme is based on a non-local interaction vertex and characterized by an infrared divergent form factor. We show that the Lorentz covariant $T^{\star}$-product is consistently defined and the energy-momentum conservation is preserved in perturbation theory if the path integral is suitably defined for this non-local theory, although unitarity is generally lost. It is illustrated that T violation is realized in the decay and formation processes. It is also argued that the equality of masses and decay widths of the particle and anti-particle is preserved if the non-local CPT violation is incorporated either directly or as perturbation by starting with the conventional CPT-even local Lagrangian. However, we also explicitly show that the present non-local scheme can induce the splitting of particle and anti-particle mass eigenvalues if one considers a more general class of Lagrangians.Comment: 28 pages; note added in proof; version published in Eur. Phys. J. C (2013) 73: 234

N=1 Super-τ3\tau_{3}QED from Atiyah-Ward Space-Time

In this letter, we present the action for the massive super-{\QED}. A pair of chiral and a pair of anti-chiral superfields with opposite U(1)-charges are required. We also carry out a dimensional reduction {\it{\`a la}} Scherk from (2+2) to (1+2) dimensions, and we show that, after suitable truncations are performed, the supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ naturally comes out.Comment: 9 pages (latex

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

Abstract 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 μ — 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