Finite Temperature Quark Confinement

Abstract

Confinement may be more easily demonstrated at finite temperature using the Polyakov loop than at zero temperature using the Wilson loop. A natural mechanism for confinement can arise via the coupling of the adjoint Polyakov loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation of the effective potential for SU(2) gluons in a background field consisting of a non-zero color magnetic field and a non-trivial Polyakov loop. The color magnetic field drives the Polyakov loop to non-trivial behavior, and the Polyakov loop can remove the well-known tachyonic mode associated with the Saviddy vacuum. Minimizing the real part of the effective potential leads to confinement, as determined by the Polyakov loop. Unfortunately, we cannot arrange for simultaneous stability and confinement for this simple class of field configurations. We show for a large class of abelian background fields that at one loop tachyonic modes are necessary for confinement.

15 pages, 7 figures, RevTeX

Cited by in corpus (15)

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• Running coupling at finite temperature and chiral symmetry restoration in QCD
• Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD
• Complete High Temperature Expansions for One-Loop Finite Temperature Effects
• Gluon condensation and scaling exponents for the propagators in Yang-Mills theory
• Thermodynamic instabilities in dynamical quark models with complex conjugate mass poles
• The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop
• Effective action for the order parameter of the deconfinement transition of Yang-Mills theories
• Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transition
• Magnetic and Thermodynamic Stability of SU(2) Yang-Mills Theory
• Polyakov Loops, Z(N) Symmetry, and Sine-Law Scaling
• Confinement at Weak Coupling
• Landau-Ginsberg Theory of Quark Confinement
• Free Energy of an SU(2) Model of (2+1)-dimensional QCD in the Constant Condensate Background