Publications (117)
 [Show abstract] [Hide abstract] ABSTRACT: In order to construct a gauge invariant twopoint function in a YangMills theory, we propose the use of the allorder 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 GribovZwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative 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.

Article: Gluons at finite temperature
[Show abstract] [Hide abstract] ABSTRACT: The gluon propagator is investigated at finite temperature via lattice simulations. In particular, we discuss its interpretation as a massivetype 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: Deconfinement and chiral transition in AdS/QCD wall models supplemented with a magnetic field
[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.  [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.
 [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 oneloop relation between ghost and gluon propagators, considering a treelevel ghostgluon vertex and our previously obtained gluonpropagator results [A. Cucchieri et al., Phys. Rev. D 85, 094513 (2012). Although this oneloop expression is not a good description of the data, it leads to a oneparameter fit of our ghostpropagator 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 oneloop predictions.
 [Show abstract] [Hide abstract] ABSTRACT: We present a local setup for the recently introduced BRSTinvariant formulation of YangMills 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 BRSTsymmetric 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 gaugeparameter independence of all correlation functions of local BRSTinvariant operators.
 [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 θvacuum (Veneziano ghost) and color confinement (no physically observable gluons). We discuss some subtleties concerning gauge (BecchiRouetStoraTuytin) 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.
 [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. Nonperturbative effects are taken into account via the socalled Refined GribovZwanziger 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 BecchiRouetStoraTyutin (BRST) symmetry, through a recently introduced nonperturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our nonperturbative definition of the linear covariant gauge.
 [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 spacetime dimensions. Our proposed form for G(p^2) is derived from the oneloop relation between ghost and gluon propagators, considering a treelevel ghostgluon vertex and our previously obtained gluonpropagator results \cite{Cucchieri:2011ig}. Although this oneloop expression is not a good description of the data, it leads to a oneparameter fit of our ghostpropagator 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 oneloop predictions.

Article: Confinement and dynamical chiral symmetry breaking in a nonperturbative renormalizable quark model
[Show abstract] [Hide abstract] ABSTRACT: Inspired by the construction of the GribovZwanziger 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.  [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 HawkingPage 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.
 [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 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 \thetavacuum (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.
 [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 momentumdependence 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.
 [Show abstract] [Hide abstract] ABSTRACT: We point out the existence of a nonperturbative exact nilpotent BRST symmetry for the GribovZwanziger 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.

Article: Confinement interpretation in a YangMills + Higgs theory when considering Gribov's ambiguity
[Show abstract] [Hide abstract] ABSTRACT: This work presents concisely the results obtained from the analysis of the twopoint 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. Nonperturbative effects are considered by taking into account the Gribov ambiguity. In general, in both YangMills models the gluon propagator has nontrivial contributions of physical and nonphysical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Nonperturbative Quantum Field Theory, which took place in SophiaAntipolis  France.  [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 GribovZwanziger (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 energystyle 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 GribovZwanziger 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 GribovZwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported.
 [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 CucchieriMendes bounds on the inverse FaddeevPopov operator at the level of the path integral quantization. Secondly, we give an explicit renormalizable prescription to implement the socalled Landau Bgauges as introduced by Maas.
 [Show abstract] [Hide abstract] ABSTRACT: We discuss a method to extract the K\"all\'enLehmann 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 Landaugauge gluon propagator at finite temperature as a massivetype bosonic propagator.
 [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 CucchieriMendes bounds on the inverse FaddeevPopov operator at the level of the path integral quantization. Secondly, we give an explicit renormalizable prescription to implement the socalled Landau Bgauges as introduced by Maas.
 [Show abstract] [Hide abstract] ABSTRACT: By evaluating the socalled Boseghost propagator, we present the first numerical evidence of BRSTsymmetry breaking for YangMills theory in minimal Landau gauge, i.e. due to the restriction of the functional integration to the first Gribov region in the GribovZwanziger approach. Our data are well described by a simple fitting function, which can be related to a massive gluon propagator in combination with an infraredfree (FaddeevPopov) ghost propagator. As a consequence, the Boseghost 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.
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19702013

Ghent University
 Department of Physics and Astronomy
Gand, Flemish, Belgium


20082009

Massachusetts Institute of Technology
 Center for Theoretical Physics
Cambridge, Massachusetts, United States
