Resumo em Inglês:

We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRST-invariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k² at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

Resumo em Inglês:

In a functional approach to QCD the infrared behaviour of Landau gauge Green functions is investigated. It can be proven that the ghost Dyson-Schwinger equation implies the Gribov-Zwanziger horizon condition. Its relation to the Kugo-Ojima confinement scenario is elucidated. Positivity violation for gluons is demonstrated, and the analytic structure of the gluon propagator is studied. Quark confinement is related to an infrared divergence of the quark-gluon vertex. It is shown that in the latter various components are non-vanishing due to the dynamical breaking of chiral symmetry. As a result an infrared finite running coupling in the Yang-Mills sector is derived whereas the running coupling related to the quark-gluon vertex is infrared divergent. In Coulomb gauge QCD already the one-gluon-exchange (over-)confines. This leads to a vanishing quark propagator, and thus quarks are confined. Nevertheless colour singlet quantities derived from the quark propagator are well-defined. Especially the expression for the quark condensate proves that chiral symmetry is dynamically broken. As expected the properties of mesons can be directly calculated whereas the mass of coloured diquarks diverges, and thus diquarks are confined. The latter nevertheless possess a well-defined size. In the third part the results obtained so far will be used to formulate a covariant Faddeev approach to nucleons. The resulting amplitudes describe the quark core of the nucleon. Besides the mass of this state also the electromagnetic form factors are calculated. The results for charge radii and magnetic moments as a function of the quark current mass provide some indication what the missing pion cloud may contribute to the nucleons' properties.

Resumo em Inglês:

We discuss the relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional vacuum defects, like monopoles, center vortices. There is certain resemblance to dual strings, domain walls considered in the continuum version of Yang-Mills theories.

Resumo em Inglês:

Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the unquenched SU(3) configurations produced by the MILC collaboration and compared with quenched gauge configurations of SU(2) first copy of the overrelaxation gauge fixing, the parallel tempering (PT) gauge fixing and quenched SU(3) 56(4) configurations. We measure the color symmetric and the color antisymmetric ghost propagator and the Binder cumulant of the l¹ norm and the l² norm of color antisymmetric ghost propagators and investigate deviation from those of Gaussian distributions. In the first copy samples of quenched SU(2) we observe a large fluctuation in the Binder cumulant at the lowest momentum point. This fluctuation is reduced in the PT gauge fixed samples. The color anti-symmetric ghost propagator of quenched SU(3) configurations depends on the lattice size and is small as compared to the symmetric one in the large lattice of 56(4). The Binder cumulants of the quenched SU(2) and the Nf = 2 + 1 unquenched SU(3) are almost consistent with 3-d and 8-d Gaussian distribution, respectively. A comparison of the SU(3) unquenched configurations and quenched configurations indicates that the dynamical quarks have the effect of making color antisymmetric ghost propagator closer to the Gaussian distribution and the Kugo-Ojima color confinement parameter c closer to 1.

Resumo em Inglês:

We report on recent numerical computations of the Landau gauge gluon and ghost propagators as well as of the ghost-gluon-vertex function in pure SU(3) Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to the low momentum region. In particular, we present new data for the gluon propagator at momenta below 300 MeV. We also discuss different systematic effects as there are finite-size, lattice discretization and Gribov copy but also unquenching effects. A MOM-scheme running coupling alphas(q²) based on the ghost-gluon vertex is calculated and found to decrease for momenta below 550 MeV, even though the renormalization constant of the vertex deviates only weakly from being constant.

Resumo em Inglês:

We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution (q²)²kappa of the Dyson-Schwinger equations is investigated and the exponent kappa is measured. The lattice data favours kappa ~ 0.52, which would imply a vanishing zero momentum gluon propagator as predicted by the Kugo-Ojima confinement mechanism and the Zwanziger horizon condition. Results for the ghost propagator and for the running coupling constant are shown.

Resumo em Inglês:

The order and the universality class of the deconfining phase transition can provide insight into the mechanism of color confinement, in particular for Nf = 2. The mechanism of confinement by monopole condensation is reviewed.

Resumo em Inglês:

The configuration space of SU(N) gauge theory is restricted to orbits with vanishing Polyakov loops of non-trivial N-ality. A practical method of constraining to this orbit space C0 is found by implementing a certain axial-type gauge. It is shown that the representative of an orbit in C0 is unique in this gauge up to time independent Abelian gauge transformations. The restricted orbit space does not admit non-Abelian monopoles. As long as C0 is thermodynamically stable, the free energy of the constrained SU(N) gauge model is of order N0 (even in the presence of dynamical quarks) and confinement is manifest for sufficiently large N. With a free energy of order N0 and Polyakov loops that vanish by design, there is no transition that deconfines color charge in such an SU(N) model. However, a proliferation of massless hadronic states of arbitrary spin could lead to a Hagedorn transition[1] if the string tension vanishes at a finite temperature T H. Constraining the orbit space to C0 can be viewed as a particular boundary condition, and T H in general is above the first order deconfinement transition of the full theory at Td. Between Td and T H a superheated confining phase may exist for SU(N > 2). Perturbation theory in C0 is sketched. It does not suffer from the severe IR-divergences observed by Linde[2]for the ordinary high temperature expansion. Correlations of the lowest transverse Abelian Matsubara modes develop a renormalization group invariant pole of second order at vanishing spatial momentum transfer when T = T H. The latter could be associated with linear confinement.

Resumo em Inglês:

Non-perturbative properties of QCD, such as color confinement, are encoded in the infrared behavior of correlation functions, e.g. propagators and vertices. Various analytic predictions have been suggested for these quantities in various gauges. Here we numerically test these predictions using lattice gauge theory. In particular, we present results for the 2- and 3-point functions for SU(2) Landau-gauge Yang-Mills theory in three and in four dimensions. Special attention is paid to systematic finite-volume effects. The gluon and ghost propagators are also evaluated in the so-called interpolating gauge (between the Landau and the Coulomb gauge), in order to study their gauge-dependence. Finally, we consider these propagators in Landau gauge at finite temperature, with the aim of understanding the effect of the deconfinement phase transition on their infrared behavior. All our results are compatible with the so-called Gribov-Zwanziger confinement scenario.

Resumo em Inglês:

We review recent one and two loop ${\overline{\mbox{MS}}}$ Landau gauge calculations using the Gribov-Zwanziger Lagrangian. The behaviour of the gluon and Faddeev-Popov ghost propagators as well as the renormalization group invariant effective coupling constant is examined in the infrared limit.

Resumo em Inglês:

We report on the nonlocal gauge invariant operator of dimension two, FµN (D²)-1 FµN. We are able to localize this operator by introducing a suitable set of (anti)commuting antisymmetric tensor fields. Starting from this, we succeed in constructing a local gauge invariant action containing a mass parameter, and we prove the renormalizability to all orders of perturbation theory of this action in the linear covariant gauges using the algebraic renormalization technique. We point out the existence of a nilpotent BRST symmetry. Despite the additional (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories by making use of an extra symmetry in the massless case. We also present explicit renormalization group functions at two loop order in the ${\overline{\mbox{MS}}}$ scheme.

Resumo em Inglês:

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is presented.

Resumo em Inglês:

We investigate the QCD Dirac operator with gauge configurations given by a liquid of instantons in the region of temperatures about the chiral phase transition. Both the quenched and unquenched cases are examined in detail. We present evidence of a localization transition in the low lying modes of the Dirac operator around the same temperature as the chiral phase transition. Thus both level statistics and eigenvectors of the QCD Dirac operator at the chiral phase transition have similar properties than those of a disordered conductor at the metal-insulator transition. This strongly suggests the phenomenon of Anderson localization (localization by destructive quantum interference) is the leading physical mechanism in the restoration of the chiral symmetry. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.

Resumo em Inglês:

Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of the vacuum and confinement through the condensation of magnetic monopoles and vortices. Other applications are related to the role of these topological excitations, nonhomogeneous solutions of the field equations, in phase transitions associated to spontaneous symmetry breaking in gauge theories, whose study is of importance, for instance, in phase transitions in the early universe. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The derivation of the nontrivial contribution of these vacuum excitations to phase transitions and its analogy with superconductivity is then made possible and they are studied here.

Resumo em Inglês:

We use the linear delta expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical temperature, chemical potential and fermionic mass which include finite N corrections. Our results seem to improve over the traditional large-N predictions.

Resumo em Inglês:

The scattering of charmed mesons on nucleons is investigated within a chiral quark model inspired on the QCD Hamiltonian in Coulomb gauge. The microscopic model incorporates a longitudinal Coulomb confining interaction derived from a self-consistent quasi-particle approximation to the QCD vacuum, and a traverse hyperfine interaction motivated from lattice simulations of QCD in Coulomb gauge. From the microscopic interactions at the quark level, effective meson-baryon interactions are derived using a mapping formalism that leads to quark-Born diagrams. As an application, the total cross-section of heavy-light D-mesons scattering on nucleons is estimated.

Resumo em Inglês:

We discuss some recent phenomenological models for strong interactions based on the idea of gauge/string duality. A very good estimate for hadronic masses can be found by placing an infrared cut off in AdS space. Considering static strings in this geometry one can also reproduce the phenomenological Cornell potential for a quark anti-quark pair at zero temperature. Placing static strings in an AdS Schwarzschild space with an infrared cut off one finds a transition from a confining to a deconfining phase at some critical horizon radius (associated with temperature).

Resumo em Inglês:

We study the N-component (2+1)-dimensional Gross-Neveu model bounded between two parallel planes separated by a distance L at finite temperature (T). We obtain a closed expression for the large-N effective coupling constant g = g(L,T,lambda). Different behavior depending on the magnitude of the fixed coupling constant lambda is found to lead to a ''critical'' value lambdac. If lambda < lambdac, only short-distance and/or high-temperature asymptotic freedom is found. For lambda > lambdac one also observes spatial confinement, which is destroyed by temperature effects. We find a confining length, Lc ~ 1.61 fm, that is close to the proton charge diameter ( ~ 1.74 fm) and a deconfining temperature, ~ 138 MeV, which is comparable to the estimated value of ~ 200 MeV for hadrons.

Resumo em Inglês:

We construct an effective model for the chiral field and the Polyakov loop in which we can investigate the interplay between the approximate chiral symmetry restoration and the deconfinement of color in a thermal SU(3) gauge theory with three flavors of massive quarks. The phenomenological couplings between these two sectors can then be related to the recent lattice data on the renormalized Polyakov loop and the chiral condensate close to the critical region.

Resumo em Inglês:

We show that QED radiative corrections change the propagator of a charged Dirac particle so that it acquires a fractional anomalous exponent connected with the fine structure constant. The result is a nonlocal object which represents a particle with a roughened trajectory whose fractal dimension can be calculated. This represents a significant shift from the traditional Wigner notions of asymptotic states with sharp well-defined masses. Non-Abelian long-range fields are more difficult to handle, but we are able to calculate the effects due to Newtonian gravitational corrections. We suggest a new approach to confinement in QCD based on a particle trajectory acquiring a fractal dimension which goes to zero in the infrared as a consequence of self-interaction, representing a particle which, in the infrared limit, cannot propagate.

Resumo em Inglês:

We define a regularization for the energy divergences in Coulomb gauge. It gives a perturbative algorithm for well-defined computations for the pure non-Abelian Yang-Mills theory in this gauge.

Resumo em Inglês:

We report on some recent solutions of the Dyson-Schwinger equations for the infrared behavior of the gluon propagator and coupling constant, discussing their differences and proposing that these different behaviors can be tested through hadronic phenomenology. We discuss which kind of phenomenological tests can be applied to the gluon propagator and coupling constant, how sensitive they are to the infrared region of momenta and what specific solution is preferred by the experimental data.

Resumo em Inglês:

The ambiguities associated with the lack of gauge invariance in the non-perturbative truncations of Schwinger-Dyson equations (SDEs) are a challenging problem which has not yet been resolved in a decisive fashion. Pursuing this aim, we study dynamical chiral symmetry breaking in quantum electrodynamics in three space-time dimensions (QED3). We investigate the gauge dependence of the chiral condensate both in the quenched and the unquenched versions of the theory and emphasize the importance of taking into account the gauge covariance properties of the fermion propagator as dictated by its Landau-Khalatnikov-Fradkin transformation (LKFT). We present numerical solutions of the SDE of the fermion propagator which respect Ward-Green-Takahashi identities (WGTI) and LKFT simultaneously. As a striking consequence, we obtain a practically gauge independent chiral condensate.

Resumo em Inglês:

The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. By following Gribov's original approach, extended to the maximal Abelian gauge, we are able to show that the diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component is found to be of the Yukawa type, with a dynamical mass originating from the dimension two gluon condensate, which is also taken into account. Furthermore, the off-diagonal ghost propagator exhibits infrared enhancement. Finally, we make a comparison with available lattice data.