arXiv subjects

D. Vercauteren

Publications and source records attributed to D. Vercauteren.

16 recordsLinked to original sources

arXiv2022

Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement

We consider a BRST invariant generalization of the "massive background Landau gauge", resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input but it enters as a result of dimensional transmutation via a BRST invariant dimension two gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program which fixes the value of the mass parameter to values close to those obtained within the Curci-Ferrari approach. Using a self-consistent background field, we can include the Polyakov loop and probe the deconfinement transition, including its interplay with the condensate and its electric-magnetic asymmetry. We report a continuous phase transition at Tc ~ 0.230 GeV in the SU(2) case and a first order one at Tc ~ 0.164 GeV in the SU(3) case, values which are again rather close to those obtained within the Curci-Ferrari model at one-loop order.

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arXiv2021

Regimes of $3D$ Yang--Mills theory in the presence of a constant vector background

In this paper, we take into account the Gribov copies present in 3D Yang-MIlls-Higgs theory with a constant vector background whose presence breaks the Lorentz symmetry. The constant vector background is introduced within the non-Abelian aether term. Here, we show that this term arises as a one-loop correction. The influence of the aether coupling constant on the system is treated afterwards. As a result, we find that for some values of it the theory can be driven from a nonperturbative regime to a perturbative one. In this paper, we work with the Higgs field in the fundamental representation and in the Landau gauge.

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arXiv2020

Non-Abelian extension of the aether term and the Gribov problem

In this paper, we treat the proper path integral quantization of the Yang-Mills-aether (YM-aether) system by dealing with the extra gauge copies in the Landau gauge. Within Gribov's prescription to get rid of such remaining gauge copies, we explicitly derive the Gribov parameter dependence of the coupling constant and of the Lorentz violation aether term. The ultraviolet limit is investigated under the light of recent bounds on the magnitude of the non-Abelian aether parameter, and we show that the Gribov parameter can be disregarded in that limit.

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arXiv2019

The BRST-invariant vacuum state of the Gribov-Zwanziger theory

We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work.

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arXiv2018

Gauge copies in the Landau-DeWitt gauge: a background invariant restriction

The Landau background gauge, also known as the Landau-DeWitt gauge, has found renewed interest during the past decade given its usefulness in accessing the confinement-deconfinement transition via the vacuum expectation value of the Polyakov loop, describable via an appropriate background. In this Letter, we revisit this gauge from the viewpoint of it displaying gauge (Gribov) copies. We generalize the Gribov-Zwanziger effective action in a BRST and background invariant way; this action leads to a restriction on the allowed gauge fluctuations, thereby eliminating the infinitesimal background gauge copies. The explicit background invariance of our action is in contrast with earlier attempts to write down and use an effective Gribov-Zwanziger action. It allows to address certain subtleties arising in these earlier works, such as a spontaneous and thus spurious Lorentz symmetry breaking, something which is now averted.

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arXiv2017

Double non-perturbative gluon exchange: an update on the soft Pomeron contribution to pp scattering

We employ a set of recent, theoretically motivated, fits to non-perturbative unquenched gluon propagators to check in how far double gluon exchange can be used to describe the soft sector of pp scattering data (total and differential cross section). In particular, we use the refined Gribov--Zwanziger gluon propagator (as arising from dealing with the Gribov gauge fixing ambiguity) and the massive Cornwall-type gluon propagator (as motivated from Dyson-Schwinger equations) in conjunction with a perturbative quark-gluon vertex, next to a model based on the non-perturbative quark-gluon Maris-Tandy vertex, popular from Bethe-Salpeter descriptions of hadronic bound states. We compare the cross sections arising from these models with "older" ISR and more recent TOTEM and ATLAS data. The lower the value of total energy \sqrt{s}, the better the results appear to be.

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arXiv2016

Exploring center vortices in SU(2) and SU(3) relativistic Yang-Mills-Higgs models

We develop numerical tools and apply them to solve the relativistic Yang--Mills--Higgs equations in a model where the SU(N) symmetry is spontaneously broken to its center. In SU(2) and SU(3), we obtain the different field profiles for infinite and finite center vortices, with endpoints at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of SU(2) fields leads us to a reference point where an Abelian-like BPS bound is reconciled with N-ality.

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arXiv2015

Confinement interpretation in a Yang-Mills + Higgs theory when considering Gribov's ambiguity

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.

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arXiv2015

Effect of the Gribov horizon on the Polyakov loop and vice versa

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.

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arXiv2014

Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge

The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.

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arXiv2014

Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge

The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The non-renormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three loop calculation.

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arXiv2014

The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter

It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang-Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev-Popov approach fails. Recent results, derived from functional tools (Dyson-Schwinger equations or exact RG) or the effective Gribov-Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cfr. the experimental success of the electroweak model based on a SU(2) x U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev-Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2) x U(1) gauge-Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin-Shenker insights about the phase diagram.

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arXiv2013

SU(2) x U(1) Yang-Mills theories in 3d with Higgs field and Gribov ambiguity

We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value nu, of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small non-Abelian coupling g and sufficiently large nu, the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and nu, we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth.

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arXiv2013

Semiclassical analysis of the phases of 4d SU(2) Higgs gauge systems with cutoff at the Gribov horizon

We present an analytical study of continuum 4d SU(2) gauge Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at analytically probing the renowned predictions of Fradkin & Shenker on the phase diagram in terms of confinement versus Higgs behaviour, obtained for the lattice version of the model. We work in the Landau version of the 't Hooft R_ξgauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime of small gauge coupling constant g and large Higgs vacuum expectation value v, there is a Higgs phase with Yukawa gauge boson propagators without Gribov effects. For a small value of the Higgs vev v and/or large g, we enter a region with Gribov type propagators that have no physical particle interpretation: the gauge bosons are as such confined. The transition between both behaviours is found to be continuous. In the adjoint case, we find evidence of a more drastic transition between the different behaviours for the propagator of the off-diagonal gauge bosons, whereas the "photon", i.e. the diagonal component of the gauge field, displays a propagator of the Gribov type. In the limit of infinite Higgs condensate, we show that a massless photon is recovered. We compare our findings with those of Fradkin & Shenker as well as with more recent numerical lattice simulations of the fundamental Higgs model. We also carefully discuss in which region of the parameter space (v,g) our approximations are trustworthy.

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arXiv2010

The asymmetry of the dimension 2 gluon condensate: the finite temperature case

In this paper, we continue the work begun in a previous article. We compute, in the formalism of local composite operators, the value of the asymmetry in the dimension two condensate for finite temperatures. We find a positive value for the asymmetry, which disappears when the temperature is increased. We also compute the value of the full dimension two condensate for higher temperatures, and we find that it decreases in absolute value, finally disappearing for sufficiently high temperature. We also comment on the temperature dependence of the electric and magnetic components of the condensate separately. We compare our results with the corresponding lattice date found by Chernodub and Ilgenfritz.

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arXiv2009

The asymmetry of the dimension 2 gluon condensate: the zero temperature case

We provide an algebraic study of the local composite operators A_μA_ν-δ_{μν}/d A^2 and A^2, with d=4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A_μA_νinto its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for \neq 0, together with =0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

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