A novel background field approach to the confinement-deconfinement transition

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 lattice results in the range $[0,2T_c]$.

13 pages, 5 figures

References in corpus (10)

• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• SU(N) gauge theories at large N
• Infrared propagators of Yang-Mills theory from perturbation theory
• Renormalized Polyakov loops in many representations
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Dual quark condensate and dressed Polyakov loops
• Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• The phase structure of QCD for heavy quarks
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model

Cited by in corpus (8)

• Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders
• Small parameters in infrared QCD: The pion decay constant
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• QCD phase diagram from the gluon propagator at finite temperature and density
• Proper constituent gluon mass as the final piece to construct hybrid mesons
• A window on infrared QCD with small expansion parameters
• Massive Gauge Theory with Quasigluon for Hot $SU(N)$: Phase Transition and Thermodynamics
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD