L. C. Q. Vilar

On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach

We investigate the quantum effects of the nonlocal gauge invariant operator 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 (Blaschke et al (2009 Eur. Phys. J. C 62 433–43)). 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 conduct a complete BRST algebraic study of the renormalizability of the theory, following Zwanzigers method of localization of nonlocal operators in QFT.

Perturbative beta function of N = 2 super Yang-Mills theories

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 phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.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 phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.

Renormalizability of nonrenormalizable field theories

UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fi ´sica Teorica, Rua Sa˜o Francisco Xavier, 524, 20550-013,Maracana˜, Rio de Janeiro, Brazil~Received 8 December 1998; published 3 May 1999!We give a simple proof of the equivalence theorem, stating that two field theories related by nonlinear fieldtransformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable fieldtheories which are actually physically equivalent to renormalizable ones. Our strategy is to show by means ofthe Becchi-Rouet-Stora formalism that the ‘‘nonrenormalizable’’ part of such fake nonrenormalizable theoriesis a kind of gauge fixing, being confined in the cohomologically trivial sector of the theory.@S0556-2821~99!50112-4#PACS number~s!: 11.10.Gh

An Algebraic criterion for the ultraviolet finiteness of quantum field theories

An algebraic criterion for the vanishing of the beta function for renormalizable quantum field theories is presented. Use is made of the descent equations following from the Wess-Zumino consistency condition. In some cases, these equations relate the fully quantized action to a local gauge invariant polynomial. The vanishing of the anomalous dimension of this polynomial enables us to establish a non-renormalization theorem for the beta function βg, stating that if the one-loop order contribution vanishes, then βg will vanish to all orders of perturbation theory. As a by-product, the special case in which βg is only of one-loop order, without further corrections, is also covered. The examples of the N = 2,4 supersymmetric Yang-Mills theories are worked out in detail.

BRST cohomology of N = 2 super-Yang-Mills theory in four dimensions

The BRST cohomology of the N = 2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N = 2 algebra. By the introduction of a set of suitable constant ghosts associated with the generators of N = 2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N = 2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge-invariant polynomial tr 2 and the complete N = 2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N = 2 β-function.

Vector supersymmetry of two-dimensional Yang-Mills theory

The vector supersymmetry of the two-dimensional (2D) topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behaviour of the theory are analysed.

Renormalizable noncommutative U(1) gauge theory without IR/UV mixing

We investigate the quantum effects of the nonlocal gauge invariant operator 1 D Fμν ∗ 1 D F 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 (hep − th/0901.1681v1). 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 also give strong reasons for our belief in that this kind of nonlocal action will not work in the general U(N) case, which will require a deeper analysis. ∗mbschlee@terra.com.br, ozemar@cefetes.br, vitor@dft.if.uerj.br

Large-mass behaviour of loop variables in abelian Maxwell-Chern-Simons theory

The large-mass behaviour of loop variables in Maxwell-Chern-Simons theory is analysed by means of a gauge-field transformation which allows us to reset the Maxwell-Chern-Simons action to pure Chern-Simons.

Gribov condition as a phase transition

Our goal will be the description of a theory of Gribovs type as a physical process of phase transition in the context of a spontaneous symmetry breaking. We mainly focus at the quantum stability of the whole process.

The Seiberg-Witten map for the 4D noncommutative BF theory

We describe the Seiberg–Witten map taking the 4D noncommutative BF theory (NCBF) into its pure commutative version. The existence of this map is in agreement with the hypothesis that such maps are available for any noncommutative theory with Schwarz-type topological sectors, and represents a strong indication for the renormalizability of these theories in general.