Algebraic renormalization of N=2 Super Yang-Mills theories coupled to matter

We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, therefore it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides to unphysical renormalizations of the quantum fields, we find that the only coupling constant of $N=2$ SYMs can get quantum corrections. Moreover we prove that all the symmetries defining the theory are algebraically anomaly--free.Comment: typing error in eq. (A.9) correcte

Chiral Current Algebras in Three--Dimensional Bf--Theory with Boundary

We consider the three--dimensional BF--model with planar boundary in the axial gauge. We find two--dimensional conserved chiral currents living on the boundary and satisfying Kac--Moody algebras.Comment: 18 page

Massive gravity and Fierz-Pauli theory

Linearized gravity is considered as an ordinary gauge field theory. This implies the need for gauge fixing in order to have well defined propagators. Only after having achieved this, the most general mass term is added. The aim of this paper is to study of the degrees of freedom of the gauge fixed theory of linearized gravity with mass term. The main result is that, even outside the usual Fierz-Pauli constraint on the mass term, it is possible to choose a gauge fixing belonging to the Landau class, which leads to a massive theory of gravity with the five degrees of freedom of a spin two massive particle.Comment: 12 pages, no figure

Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz-Pauli massive gravity)

In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles (ghosts). We find several possibilities, depending on the choice of the gauge fixing term. {Amongst these, two solutions with good massless limit are found.} The request of the absence of ghosts, alone, does not isolate the Fierz-Pauli case: several examples of massive theories, which may include or not the Fierz-Pauli mass term, are given. On the other hand, the Fierz-Pauli theory can be uniquely identified by means of a symmetry: it turns out the the Fierz-Pauli massive gravity is the only element of the cohomology of a BRS operator.Comment: 18 pages, minor changes, refs adde

Infrared Regularization of Yang-Mills Theories

We introduce an infrared regulator in Yang--Mills theories under the form of a mass term for the nonabelian fields. We show that the resulting action, built in a covariant linear gauge, is multiplicatively renormalizable by proving the validity at all orders of the Slavnov identity defining the theory.Comment: final version to appear in Mod.Phys.Lett.A. 8 pages + cover, plain LaTe

Infrared and Ultraviolet Finiteness of Topological BF Theory in Two Dimensions

The two--dimensional topological BF model is considered in the Landau gauge in the framework of perturbation theory. Due to the singular behaviour of the ghost propagator at long distances, a mass term to the ghost fields is introduced as infrared regulator. Relying on the supersymmetric algebraic structure of the resulting massive theory, we study the infrared and ultraviolet renormalizability of the model, with the outcome that it is perturbatively finite.Comment: 26 pages, GEF-TH-11/199

Repairing Broken Algebras

We consider theories characterized by a set of Ward operators which do not form a closed algebra. We impose the Slavnov--Taylor identity built out of the Ward operators and we derive the acceptable breaking of the algebra and the general form of the classical action. The 1PI generating functional is expressed in terms of the known quantities characterizing the theory and of a nontrivial integrability condition. As a nontrivial application of our formalism, we discuss the N=4 supersymmetric nonlinear sigma model.Comment: one section containing a remarkable (and unexpected) result on N=4 supersymmetric sigma model has been added. 10 pages, plain LaTeX, no figure

Perturbation Theory for Antisymmetric Tensor Fields in Four Dimensions

Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.Comment: 23 page

Algebraic Renormalization of N=2N=2 Supersymmetric Yang-Mills Chern-Simons Theory in the Wess-Zumino Gauge

We consider a N=2 supersymmetric Yang-Mills-Chern-Simons model, coupled to matter, in the Wess-Zumino gauge. The theory is characterized by a superalgebra which displays two kinds of obstructions to the closure on the translations: field dependent gauge transformations, which give rise to an infinite algebra, and equations of motion. The aim is to put the formalism in a closed form, off-shell, without introducing auxiliary fields. In order to perform that, we collect all the symmetries of the model into a unique nilpotent Slavnov-Taylor operator. Furthermore, we prove the renormalizability of the model through the analysis of the cohomology arising from the generalized Slavnov-Taylor operator. In particular, we show that the model is free of anomaly.Comment: 17 pages, latex, no figures. Computation of the cohomology corrected. Appendix adde

Non-Renormalization Properties of the Chern-Simons Action Coupled to Matter

We analyze an abelian gauge model in 3 dimensions which includes massless scalar matter fields. By controlling the trace anomalies with a local dilatation Ward identity, we show that, in perturbation theory and within the BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies, in particular, the vanishing of the corresponding $\beta$ function in the renormalization group equation.Comment: 11 page