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

Abstract

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.

35 pages, 20 figures

References in corpus (20)

• The equation of state in (2+1)-flavor QCD
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Infrared propagators of Yang-Mills theory from perturbation theory
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Renormalized Polyakov loops in many representations
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
• Chiral and deconfinement transition from Dyson-Schwinger equations
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• Equation of State of Gluon Plasma from Local Action
• The phase structure of QCD for heavy quarks
• Quark-gluon vertex from the Landau gauge Curci-Ferrari model
• Confinement order parameters and fluctuations
• Influence of Gribov ambiguities in a class of nonlinear covariant gauges
• Confinement--deconfinement phase transition and gauge-invariant gluonic mass in Yang-Mills theory
• Center symmetry and area laws
• Perturbation theory of non-perturbative QCD

Cited by in corpus (46)

• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• Existence of the critical endpoint in the vector meson extended linear sigma model
• Non-perturbative finite-temperature Yang-Mills theory
• How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?
• QCD Running Couplings and Effective Charges
• Small parameters in infrared quantum chromodynamics
• A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections
• Yang-Mills correlators across the deconfinement phase transition
• The ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections
• A novel background field approach to the confinement-deconfinement transition
• Two-loop perturbative corrections to the constrained effective potential in thermal QCD
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Variational study of mass generation and deconfinement in Yang-Mills theory
• Localized rainbows in the QCD phase diagram
• Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders
• Gluon Dynamics, Center Symmetry and the deconfinement phase transition in SU(3) pure Yang-Mills theory
• Two-loop corrections to the QCD propagators within the Curci-Ferrari model
• Calculation of the non-perturbative strong coupling from first principles
• Quark and Polyakov-loop correlations in effective models at zero and non-vanishing density
• Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
• A Gribov-Zwanziger type action invariant under background gauge transformations
• Gauge copies in the Landau-DeWitt gauge: a background invariant restriction
• Symmetry restoration and the gluon mass in the Landau gauge
• Fluctuations of order parameter in an $SU(N_c)$ effective model
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• Small parameters in infrared QCD: The pion decay constant
• Resummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
• Covariant variational approach to Yang-Mills Theory: Thermodynamics
• Collisional energy loss of a heavy quark in a semiquark-gluon plasma
• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• QCD phase diagram from the gluon propagator at finite temperature and density
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• A window on infrared QCD with small expansion parameters
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• A perturbative approach to the confinement-deconfinement phase transition
• Massive Gauge Theory with Quasigluon for Hot $SU(N)$: Phase Transition and Thermodynamics
• On the contribution of different coupling constants in the infrared regime of Yang-Mills theory: a Curci-Ferrari approach
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• The scalar sunset diagram at finite temperature with imaginary square masses
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature