Yang-Mills correlation functions at finite temperature

Fister, Leonard; Pawlowski, Jan Μ.

doi:10.48550/arxiv.1112.5440

Cited by 39 publications

(74 citation statements)

References 48 publications

(141 reference statements)

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“…Gauge-fixed lattice calculations in the Landau gauge show a strong increase of the electric susceptibility 1 at the second order phase transition of the SU(2) theory, which is not seen in continuum calculations [7,8], probably due to the lack of proper account of the order parameter mentioned above. Although the phase transition is correctly described using the self-consistent background field approach, it is not clear how to compare to those lattice results in the Landau gauge.…”

Section: Introductionmentioning

confidence: 94%

“…Indeed, for a given background Ā, the state of the system is obtained as the minimum A min [ Ā] of Γ [A, Ā] with respect to A. The symmetry identity (7) implies that, under any transformation…”

Section: The Class Of Landau-dewitt Gaugesmentioning

confidence: 99%

“…Since U c represents the same center transformation as U in G/G 0 , we deduce that Γ c [A] is invariant under center transformations. 7 In turn the minima…”

Section: Center-symmetric Effective Action and Effective Potentialmentioning

confidence: 99%

“…Such an explicit breaking of the center symmetry by the gauge-fixing procedure should not alter the physical results in principle, but this is clearly an issue when approximations are involved. That is, for instance, the case in the widely used Landau gauge, where the lack of explicit center symmetry leads to unphysical results in approximate continuum calculations, as compared to the results of gauge-fixed lattice simulations [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Note that this is not a trivial statement because Γ [ Ā] is not an effective action in the usual sense. In particular, it is not the Legendre transform of the generating functional for connected correlators 7. We stress here that Γ c [A] is not invariant under every transformation U ∈ G but, rather, under certain representatives U c of each of the transformations in G/G 0 which are the physical center transformations, where the gauge redundancy has been quotiented away.…”

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confidence: 99%

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A novel background field approach to the confinement-deconfinement transition

et al. 2022

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We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with the lattice data in the range [0,2T_c][0,2Tc].

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Section: Introductionmentioning

confidence: 94%

Section: The Class Of Landau-dewitt Gaugesmentioning

confidence: 99%

“…Since U c represents the same center transformation as U in G/G 0 , we deduce that Γ c [A] is invariant under center transformations. 7 In turn the minima…”

Section: Center-symmetric Effective Action and Effective Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A novel background field approach to the confinement-deconfinement transition

et al. 2022

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On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

Huber

Smekal

2013

J. High Energ. Phys.

104

162

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We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

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Spurious divergences in Dyson-Schwinger equations

Huber

Smekal

2014

J. High Energ. Phys.

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Abstract:We revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its DysonSchwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green's functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

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Yang-Mills correlation functions at finite temperature

Cited by 39 publications

References 48 publications

A novel background field approach to the confinement-deconfinement transition

A novel background field approach to the confinement-deconfinement transition

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

Spurious divergences in Dyson-Schwinger equations

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