An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N = 2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N = 2 Yang-Mills action and the local gauge invariant polynomial Tr φ 2 , φ(x) being the scalar field of the N = 2 vector gauge multiplet. The nonrenormalization theorem for the β g function follows from the vanishing of the anomalous dimension of Tr φ 2 .

Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is provided.Comment: 8 pages, LateX2e fil

Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field.

We investigate the quantum effects of the nonlocal gauge invariant operator 1 D 2 F µν * 1 D 2 F µν in the noncommutative U (1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out (Eur.P hys.J.C62 : 433 − 443, 2009). We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT. *

We prove that there is no power-counting renormalizable nonabelian generalization of the abelian topological mass mechanism in four dimensions. The argument is based on the technique of consistent deformations of the master equation developed by G. Barnich and one of the authors. Recent attempts involving extra fields are also commented upon.