Deconfinement transition in SU( N ) theories from perturbation theory

Reinosa, Urko; Serreau, Julien; Tissier, Matthieu; Wschebor, Nicolás

doi:10.1016/j.physletb.2015.01.006

Cited by 87 publications

(172 citation statements)

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“…Let us first start with the infinite quark mass limit, that is the pure Yang-Mills case. We find a first order phase transition at a temperature T d 185 MeV, see [5], the unique, Z 3 -symmetric minimum of V( ) at = 0 for T < T d , turning into a triplet of Z 3 -breaking minima with 0 for T > T d . The order of the transition is in agreement with the lattice predictions, even though the value for T d is somewhat below the lattice value T d 270 MeV, see for instance [8].…”

Section: Phase Structure At Imaginary Chemical Potentialmentioning

confidence: 86%

A perturbative approach to the confinement-deconfinement phase transition

Reinosa

2016

EPJ Web Conf.

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Abstract. We summarize recent progress in describing the confinement-deconfinement transition from a novel perturbative approach.The low energy regime of Quantum Chromodynamics is not accessible to standard perturbative methods based on the Faddeev-Popov gauge fixing procedure, because the corresponding running coupling becomes large at these scales and even diverges at a finite scale known as Λ QCD . To remedy these shortcomings, various non-perturbative approaches have been invented, from lattice QCD to non-perturbative continuum methods, and much progress has been achieved over the years. Here, we would like to report on yet another possible route to the low energy regime of QCD. It is based on the speculation that perturbation theory might be applicable after all, provided one takes into account modifications of the Faddeev-Popov procedure. These modifications are needed because, in most practical cases, the gauge fixing is ambiguous in the infrared due to the presence of socalled Gribov copies. Various ways of dealing with the Gribov ambiguity in the Landau gauge have been proposed in the literature but we shall focus more specifically on the proposal of [1], based on the addition of a gluon mass term to the usual Landau gauge-fixed action. 1 This modified action remains renormalizable and, interestingly, some of the corresponding RG trajectories yield a running coupling that remains bounded and effectively small, even at low energies [3] which justifies the use of perturbation theory in this regime. In particular, at one-loop, the approach has been shown to reproduce lattice results for correlation functions to a good accuracy.We shall further test the validity of this novel perturbative approach by studying the phase structure of QCD in the heavy-quark limit, for which the lattice has provided a wealth of data to compare with, including the case of a real chemical potential. In this regime, the relevant transition is the confinement-deconfinement transition, which we study by evaluating the Polyakov loop effective potential V( ,¯ ). The appropriate extremization of the latter, see below, allows us to access the actual values of the Polyakov loops (P denotes the path-oredering andP the anti-path ordering)as functions of the temperature T = 1/β. These quantities are directly related to the free energies of a static quark and a static anti-quark respectively, = e −βF q and¯ = e −βFq , and are thus order parametersBased on various works in collaboration with Julien Serreau, Matthieu Tissier and Nicolás Wschebor. e-mail: urko.reinosa@polytechnique.edu 1 We refer to [2] and references therein for details on the so-called (refined) Gribov-Zwanziger approach.

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Section: Phase Structure At Imaginary Chemical Potentialmentioning

confidence: 86%

A perturbative approach to the confinement-deconfinement phase transition

Reinosa

2016

EPJ Web Conf.

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“…Moreover, in order to explicitly compute the Polyakov loop in our model one could compute its effective potential in the background field formalism (for recent pure glue studies, see Refs. [58][59][60] and Ref. [61] for the case with heavy quarks).…”

Section: Summary and Discussionmentioning

confidence: 99%

Thermodynamics of an exactly solvable confining quark model

2015

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The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.

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“…In Sect. 3, the Polyakov loop is introduced into the GZ theory via the background field method, building on work of other people [27,28,32]. Next, Sect.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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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 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. a

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Deconfinement transition in SU( N ) theories from perturbation theory

Cited by 87 publications

References 50 publications

A perturbative approach to the confinement-deconfinement phase transition

A perturbative approach to the confinement-deconfinement phase transition

Thermodynamics of an exactly solvable confining quark model

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

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