The infrared behavior of the gluon and ghost propagators in SU(2) Yang-Mills theory in the maximal Abelian gauge

We report on some recent analytical results on the behaviour of the gluon and ghost propagators in Euclidean SU(2) Yang-Mills theory quantized in the maximal Abelian gauge (MAG). This gauge is of particular interest for the dual superconductivity picture to explain color confinement. Two kinds of effects are taken into account: those arising from a treatment of Gribov copies in the MAG and those arising from a dynamical mass originating in a dimension two gluon condensate. The diagonal component of the gluon propagator displays the typical Gribov-type behaviour, while the off-diagonal component is of the Yukawa type due to the dynamical mass. These results are in qualitative agreement with available lattice data on the gluon propagators. The off-diagonal ghost propagator exhibits an infrared enhancement due to the Gribov restriction, while the diagonal one remains unaffected.Comment: 6 pages. Talk given by S.P. Sorella at the "I Latin American Workshop on High Energy Phenomenology (I LAWHEP)", December 1-3 2005, Instituto de Fisica, UFRGS, Porto Alegre, Rio Grande Do Sul, Brasi

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.Comment: final version, to appear in Physical Review

Modified gauge unfixing formalism and gauge symmetries in the non-commutative chiral bosons theory

We use the gauge unfixing (GU) formalism framework in a two dimensional noncommutative chiral bosons (NCCB) model to disclose new hidden symmetries. That amounts to converting a second-class system to a first-class one without adding any extra degrees of freedom in phase space. The NCCB model has two second-class constraints -- one of them turns out as a gauge symmetry generator while the other one, considered as a gauge-fixing condition, is disregarded in the converted gauge-invariant system. We show that it is possible to apply a conversion technique based on the GU formalism direct to the second-class variables present in the NCCB model, constructing deformed gauge-invariant GU variables, a procedure which we name here as modified GU formalism. For the canonical analysis in noncommutative phase space, we compute the deformed Dirac brackets between all original phase space variables. We obtain two different gauge invariant versions for the NCCB system and, in each case, a GU Hamiltonian is derived satisfying a corresponding first-class algebra. Finally, the phase space partition function is presented for each case allowing for a consistent functional quantization for the obtained gauge-invariant NCCB.Comment: 13 page

Gauge Symmetry of the Chiral Schwinger model from an improved Gauge Unfixing formalism

In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the $\alpha$ parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.Comment: 13 page

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 MSbar scheme.Comment: 24 pages. no figure

Local renormalizable gauge theories from nonlocal operators

The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator $\int A \frac{1}{D^2} A$ is analysed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.Comment: 16 page