Abstract
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].
Highlights
The method is based on a background-field generalisation of the Landau gauge with a given, center-symmetric background
Under any transformation U ∈ G, is multiplied by the corresponding center phase w, which implies that it vanishes if the symmetry group G/G0 is unbroken and that a nonzero value signals the spontaneous breaking of the center symmetry
It follows from Eq (7) that the latter is invariant under the gauge transformation of its argument, Γ[AU ] = Γ[A], for any U ∈ G, which, in particular, includes the center symmetry
Summary
The modern theory of the strong interaction, predicts a dramatic change in the behavior of thermodynamics observables at temperatures of the order of a hundred of MeV [1]. Its properties and its lattice implementation, we explicitly apply the center-symmetric gauge fixing in the context of the perturbative Curci-Ferrari (CF) approach to infrared QCD [38–41] The latter is motivated by two essential observations from lattice simulations in the Landau gauge, namely, the fact that the coupling (defined in the Taylor scheme) remains finite and under perturbative control at all scales and the fact that the gluon propagator at zero momentum is finite, corresponding to the dynamical generation of a screening mass [42–44]. It has been successfully used to compute various infrared properties of various YM and QCD-like theories in the vacuum and at nonzero temperature and density [19, 20, 22, 25, 39, 40, 45–47] In the latter case, it has been implemented in the framework of self-consistent background field techniques mentioned above and gives remarkable results already at one-loop order. We compute the Polyakov loop as a function of the temperature, which shows various improvements over a similar evaluation in the CF model using self-consistent backgrounds [19], for instance, a slower rise above the transition, in line with lattice results [48–51] as well as with results obtained within the functional renormalization group [52]
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