On Consistency Of Noncommutative Chern-Simons Theory

We consider the noncommutative extension of Chern-Simons theory. We show the the theory can be fully expanded in power series of the noncommutative parameter theta and that no non-analytical sector exists. The theory appears to be unstable under radiative corrections, but we show that the infinite set of instabilities, to all orders in \hbar and in theta, is confined to a BRS exact cocycle. We show also that the theory is anomaly free. The quantum theory cannot be written in terms of the Groenewald-Moyal star product, and hence doubts arise on the interpretation of the noncommutative nature of the underlying spacetime. Nonetheless, the deformed theory is well defined as a quantum field theory, and the beta function of the Chern-Simons coupling constant vanishes, as in the ordinary Chern-Simons theory.Comment: 17 page

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

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

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

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

Antisymmetric tensor gauge theory

We analyze to all perturbative orders the properties of two possible quantum extensions of classically on-shell equivalent antisymmetric tensor gauge models in four dimensions. The first case, related to the soft breaking of a topological theory wants a gauge field of canonical dimension one. The other possibility, which assigns canonical dimension two to the gauge field, leads to the $\sigma$ model interpretation of the theory. In both instances we find that the models are anomaly free.Comment: 28 ,Latex,GEF-TH 10/9

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