Relation between chiral symmetry breaking and confinement in YM-theories

Abstract

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab initio continuum formulation of Yang-Mills theories, and the convergence of the mode sum is studied in detail. The mode sums are then explicitly calculated for the Schwinger model and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice gauge theory, the IR dominated mode sums are considered and the mode sum approximation to the static quark anti-quark potential is obtained numerically. We find a good agreement between the mode sum approximation and the static potential at large distances for the confinement and the high temperature plasma phase.

17 pages, 10 figures, typos corrected, references added, final version to appear in PRD

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• Center vortices and the quark propagator in SU(2) gauge theory
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• Gauge-Invariant Formalism with a Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking
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• Chiral symmetry breaking and confinement: separating the scales
• Adjoint quarks and fermionic boundary conditions
• Polyakov loop fluctuations in Dirac eigenmode expansion
• Analytical Formulae of the Polyakov and the Wilson Loops with Dirac Eigenmodes in Lattice QCD
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• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Center phase transition from matter propagators in (scalar) QCD
• Gapless Dirac Spectrum at High Temperature
• Selected Issues in Thermal Field Theory
• A dual order parameter from fundamentally colour charged matter
• QCD Green's Functions and Phases of Strongly-Interacting Matter
• Properties of canonical fermion determinants with a fixed quark number