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

Canfora, FE; Dudal, David; Justo, I. F.; Pais, P.; Rosa, Luigi; Vercauteren, David

doi:10.1140/epjc/s10052-015-3546-y

Cited by 51 publications

(104 citation statements)

References 109 publications

(205 reference statements)

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“…Interestingly, similar pathologies are observed in other approaches [23,31,67] which, we believe, have the same origin as the one described here. In the present case, these spurious features disappear at NLO, where we obtain a positive entropy-a monotonously increasing pressure-at all temperatures; 22 see Figs.…”

Section: Nlo Resultssupporting

confidence: 89%

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Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

et al. 2016

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We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.

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Section: Nlo Resultssupporting

confidence: 89%

“…This has been used to study the confinement-deconfinement transition of SU(N ) theories in Refs. [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

et al. 2016

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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: 98%

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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“…Figure 6 shows the result for the ghost form factor using the "best copy" gauge fixing. The obtained ghost form factor has an IR exponent of ≃ 0.5, which is at odds with the sum rule (16) given that an IR exponent of = 1 is obtained for the lattice gluon propagator; see (20). This result is puzzling since the sum rule is considered incontrovertible as it is obtained under quite mild assumptions.…”

Section: Comparison With Lattice Calculationmentioning

confidence: 81%

“…These are based on either Dyson-Schwinger equations [2][3][4][5][6][7] or functional renormalization group flow equations [8,9], or they exploit the variational principle in either the Hamiltonian [10,11] or covariant [12,13] formulation of gauge theory. There are also semiphenomenological approaches assuming a massive gluon propagator [14] or the Gribov-Zwanziger action [15]; see [16].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

Reinhardt

Burgio

Campagnari

et al. 2018

Advances in High Energy Physics

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We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang-Mills theory, the deconfinement phase transition is found to be second order for SU(2) and first order for SU(3), in agreement with the lattice results. The corresponding critical temperatures are found to be 275 MeV and 280 MeV, respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of 198 MeV and 170 MeV, respectively, for the deconfinement and chiral transition.

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

Cited by 51 publications

References 109 publications

Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

Thermodynamics of an exactly solvable confining quark model

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

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