V. E. R. Lemes

Remarks on a class of renormalizable interpolating gauges

A class of covariant gauges allowing one to interpolate between the Landau, the maximal abelian, the linear covariant and the Curci-Ferrari gauges is discussed. Multiplicative renormalizability is proven to all orders by means of algebraic renormalization. All one-loop anomalous dimensions of the fields and gauge parameters are explicitly evaluated in the scheme.

On the SL(2,R) symmetry in Yang-Mills Theories in the Landau, Curci-Ferrari and Maximal Abelian Gauge

The existence of a SL(2; ) symmetry is discussed in SU(N) Yang-Mills in the maximal abelian gauge. This symmetry, also present in the Landau and Curci-Ferrari gauge, ensures the absence of tachyons in the maximal abelian gauge. In all these gauges, SL(2; ) turns out to be dynamically broken by ghost condensates.

Renormalizability of a quark―gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark–gluon model with soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.

Dynamical gluon mass generation from in linear covariant gauges

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator AμaAμa in linear covariant gauges. We show that the formation of AμaAμa is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.

Gluon–ghost condensate of mass dimension 2 in the Curci–Ferrari gauge

Abstract The effective potential for an on-shell BRST invariant gluon–ghost condensate of mass dimension 2 in the Curci–Ferrari gauge in SU(N) Yang–Mills is analysed by combining the local composite operator technique with the algebraic renormalization. We pay attention to the gauge parameter independence of the vacuum energy obtained in the considered framework and discuss the Landau gauge as an interesting special case.

The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory

Abstract The local composite gluon-ghost operator ( 1 2 A aμ A μ a +α c a c a ) is analysed in the framework of the algebraic renormalization in SU(N) Yang–Mills theories in the Landau, Curci–Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MS scheme for the Curci–Ferrari gauge.

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.

Study of the properties of the Gribov region in SU(N) Euclidean Yang–Mills theories in the maximal Abelian gauge

In this paper we address the issue of the Gribov copies in SU(N), N > 2, Euclidean Yang–Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similar to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonal directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension 2 condensates.

The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates

The infrared behavior of the gluon and ghost propagators is studied in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data.

Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge

The properties of the Gribov region in SU(2) Euclidean Yang-Mills theories in the maximal Abelian gauge are investigated. This region turns out to be bounded in all off-diagonal directions, while it is unbounded along the diagonal one. The soft breaking of the Becchi-Rouet-Stora-Tyutin invariance due to the restriction of the domain of integration in the path integral to the Gribov region is scrutinized. Owing to the unboundedness in the diagonal direction, the invariance with respect to Abelian transformations is preserved, a property which is at the origin of the local U(1) Ward identity of the maximal Abelian gauge.