David Dudal

Ghent University, Gand, Flemish, Belgium

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Publications (117)

  • Source
    M. A. L. Capri · D. Dudal · A. D. Pereira · [...] · S. P. Sorella
    [Show abstract] [Hide abstract] ABSTRACT: In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of <A^h A^h> are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator <A^h A^h> enables us to attach a BRST invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of <A^h A^h> as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use <A^h A^h> to probe the pole structure of the massive gauge boson in a gauge invariant fashion.
    Full-text available · Article · Nov 2016
  • P. J. Silva · O. Oliveira · D. Dudal · [...] · N. Cardoso
    [Show abstract] [Hide abstract] ABSTRACT: The gluon propagator is investigated at finite temperature via lattice simulations. In particular, we discuss its interpretation as a massive-type bosonic propagator. Moreover, we compute the corresponding spectral density and study the violation of spectral positivity. Finally, we explore the dependence of the gluon propagator on the phase of the Polyakov loop.
    Article · Nov 2016
  • [Show abstract] [Hide abstract] ABSTRACT: We discuss the phenomenon of (inverse) magnetic catalysis for both the deconfinement and chiral transition. We discriminate between the hard and soft wall model, which we suitably generalize to include a magnetic field. Our findings show a critical deconfinement temperature going down, in contrast with the chiral restoration temperature growing with increasing magnetic field. This is at odds with contemporary lattice data, so the quest for a holographic QCD model capable of capturing inverse magnetic catalysis in the chiral sector remains open.
    Article · Nov 2016
  • [Show abstract] [Hide abstract] ABSTRACT: The two point gluon and ghost correlation functions and the three gluon vertex are investigated, in the Landau gauge, using lattice simulations. For the two point functions, we discuss the approach to the continuum limit looking at the dependence on the lattice spacing and volume. The analytical structure of the propagators is also investigated by computing the corresponding spectral functions using an implementation of the Tikhonov regularisation to solve the integral equation. For the three point function we report results when the momentum of one of the gluon lines is set to zero and discuss its implications.
    Article · Nov 2016
  • [Show abstract] [Hide abstract] ABSTRACT: We present an analytic description of numerical results for the ghost propagator G(p2) in the minimal Landau gauge on the lattice. The data were produced in the SU(2) case using the largest lattice volumes to date, for d=2, 3 and 4 spacetime dimensions. Our proposed form for G(p2) is derived from the one-loop relation between ghost and gluon propagators, considering a tree-level ghost-gluon vertex and our previously obtained gluon-propagator results [A. Cucchieri et al., Phys. Rev. D 85, 094513 (2012). Although this one-loop expression is not a good description of the data, it leads to a one-parameter fit of our ghost-propagator data with a generally good value of χ2/d.o.f., comparable to other fitting forms used in the literature. At the same time, we present a simple parametrization of the difference between the lattice data and the one-loop predictions.
    Article · May 2016
  • Source
    M. A. L. Capri · D. Dudal · D. Fiorentini · [...] · S. P. Sorella
    [Show abstract] [Hide abstract] ABSTRACT: We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
    Full-text available · Article · May 2016
  • D. Dudal · M. S. Guimaraes
    [Show abstract] [Hide abstract] ABSTRACT: In this short note, we come back to the recent proposal put forward by Kharzeev and Levin [Phys. Rev. Lett. 114, 242001 (2015)], in which they phenomenologically couple the nonperturbative Veneziano ghost to the perturbative gluon, leading to a modified gluon propagator (the “glost”) of the Gribov type, with complex poles. As such, a possible link was made between the QCD topological θ-vacuum (Veneziano ghost) and color confinement (no physically observable gluons). We discuss some subtleties concerning gauge (Becchi-Rouet-Stora-Tuytin) invariance of this proposal, related to the choice of Feynman gauge. We draw particular attention to the incompatibility in the longitudinal sector with available nonperturbative results for the linear covariant gauge. We furthermore provide an example in the Landau gauge of a similar phenomenological vertex that also describes the necessary Veneziano ghost but does not affect the Landau gauge gluon propagator.
    Article · Apr 2016
  • Source
    M. A. L. Capri · D. Dudal · D. Fiorentini · [...] · S. P. Sorella
    [Show abstract] [Hide abstract] ABSTRACT: In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.
    Full-text available · Article · Mar 2016 · Physical Review D
  • Source
    [Show abstract] [Hide abstract] ABSTRACT: We present an analytic description of numerical results for the ghost propagator G(p^2) in minimal Landau gauge on the lattice. The data were produced in the SU(2) case using the largest lattice volumes to date, for d = 2, 3 and 4 space-time dimensions. Our proposed form for G(p^2) is derived from the one-loop relation between ghost and gluon propagators, considering a tree-level ghost-gluon vertex and our previously obtained gluon-propagator results \cite{Cucchieri:2011ig}. Although this one-loop expression is not a good description of the data, it leads to a one-parameter fit of our ghost-propagator data with a generally good value of \chi^2/dof, comparable to other fitting forms used in the literature. At the same time, we present a simple parametrization of the difference between the lattice data and the one-loop predictions.
    Full-text available · Article · Feb 2016
  • [Show abstract] [Hide abstract] ABSTRACT: Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the rho meson mass and decay constant.
    Article · Dec 2015
  • [Show abstract] [Hide abstract] ABSTRACT: In this paper, we study the influence of an external magnetic field in holographic QCD models where the backreaction is modeled in via an appropriate choice of the background metric. We add a phenomenological soft wall dilaton to incorporate better IR behavior (confinement). Elaborating on previous studies conducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Page transition, the dual of the deconfinement transition, as a function of the magnetic field. We confirm that the critical deconfinement temperature can drop with the magnetic field. Secondly, we study the quark condensate holographically as a function of the applied magnetic field and demonstrate that this model does not exhibit inverse magnetic catalysis at the level of the chiral transition. The quest for a holographic QCD model that qualitatively describes the inverse magnetic catalysis at finite temperature is thus still open. Throughout this work, we pay special attention to the different holographic parameters and we attempt to fix them by making the link to genuine QCD as close as possible. This leads to several unanticipated and so far overlooked complications (such as the importance of the AdS length L) that we discuss in detail.
    Article · Nov 2015
  • D. Dudal · M. S. Guimaraes
    [Show abstract] [Hide abstract] ABSTRACT: In this short note, we come back to the recent proposal put forward by Kharzeev and Levin [PRL 114 (2015) 24, 242001], in which they phenomenologically couple the non-perturbative Veneziano ghost to the perturbative gluon, leading to a modified gluon propagator (the "glost") of the Gribov type, with complex poles. As such, a possible link was made between the QCD topological \theta-vacuum (Veneziano ghost) and color confinement (no physically observable gluons). We discuss some subtleties concerning gauge (BRST) invariance of this proposal, related to the choice of Feynman gauge. We furthermore provide an example in the Landau gauge of a similar phenomenological vertex that also describes the necessary Veneziano ghost but does not affect the Landau gauge gluon propagator.
    Article · Nov 2015
  • Source
    David Dudal · Thomas G. Mertens
    [Show abstract] [Hide abstract] ABSTRACT: We point out a subtlety in choosing the radiation gauge (A(z)=0 combined with the Lorenz gauge) for gauge fields in AdS/QCD for black hole backgrounds. We then demonstrate the effect of this on the momentum-dependence of the spectral functions of the J/psi vector meson, showing a spreading with momentum and a breaking of isotropy, in contrast to previous results in the literature. We also discuss the dependence on a background magnetic field, following our earlier proposed model. (C) 2015 The Authors. Published by Elsevier B.V.
    Full-text available · Article · Oct 2015 · Physics Letters B
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    [Show abstract] [Hide abstract] ABSTRACT: We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
    Full-text available · Article · Aug 2015 · Physical Review D
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    I. F. Justo · M. A. L. Capri · D. Dudal · [...] · D. Vercauteren
    [Show abstract] [Hide abstract] ABSTRACT: This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)\times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.
    Full-text available · Article · Jun 2015
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    F. E. Canfora · David Dudal · Igor Figueiredo Justo · [...] · D. Vercauteren
    [Show abstract] [Hide abstract] ABSTRACT: We consider finite temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger (GZ) quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov loop parameter and solving the Gribov gap equation. Inspired by the Casimir energy-style of computation, we illustrate the usage of Zeta function regularization in finite temperature calculations. Our main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. In this exploratory work we mainly restrict ourselves to the original Gribov-Zwanziger quantization procedure in order to illustrate the approach and the potential direct link between the vacuum structure of the theory (dynamical mass scales) and (de)confinement. We also present a first look at the critical temperature obtained from the Refined Gribov-Zwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported.
    Full-text available · Article · May 2015 · European Physical Journal C
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    [Show abstract] [Hide abstract] ABSTRACT: In this note, we consider the Landau gauge in the continuum formulation. Our purposes are twofold. Firstly, we try to work out the consequences of the recently derived Cucchieri-Mendes bounds on the inverse Faddeev-Popov operator at the level of the path integral quantization. Secondly, we give an explicit renormalizable prescription to implement the so-called Landau B-gauges as introduced by Maas.
    Full-text available · Article · Feb 2015 · European Physical Journal C
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    Paulo J. Silva · Orlando Oliveira · David Dudal · [...] · Nuno Cardoso
    [Show abstract] [Hide abstract] ABSTRACT: We discuss a method to extract the K\"all\'en-Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau-gauge gluon propagator at finite temperature as a massive-type bosonic propagator.
    Full-text available · Article · Dec 2014 · Acta Physica Polonica B, Proceedings Supplement
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    [Show abstract] [Hide abstract] ABSTRACT: In this note, we consider the Landau gauge in the continuum formulation. Our purposes are twofold. Firstly, we try to work out the consequences of the recently derived Cucchieri-Mendes bounds on the inverse Faddeev-Popov operator at the level of the path integral quantization. Secondly, we give an explicit renormalizable prescription to implement the so-called Landau B-gauges as introduced by Maas.
    Full-text available · Article · Nov 2014
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    [Show abstract] [Hide abstract] ABSTRACT: By evaluating the so-called Bose-ghost propagator, we present the first numerical evidence of BRST-symmetry breaking for Yang-Mills theory in minimal Landau gauge, i.e. due to the restriction of the functional integration to the first Gribov region in the Gribov-Zwanziger approach. Our data are well described by a simple fitting function, which can be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. As a consequence, the Bose-ghost propagator, which has been proposed as a carrier of the confining force in minimal Landau gauge, displays a 1/p^4 singularity in the infrared limit.
    Full-text available · Article · Oct 2014