Gauge invariant effective action for the Polyakov line in the SU(N) Yang--Mills theory at high temperatures

Abstract

We integrate out fast varying quantum fluctuations around static A_4 and A_i fields for the SU(N) gauge group. By assuming that the gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4 we obtain two variants of the effective high-temperature theory for the Polyakov line. One is the effective action for the gauge-invariant eigenvalues of the Polyakov line, and it is explicitly Z(N) symmetric. The other is the effective action for the Polyakov line itself as an element of the SU(N). In this case the theory necessarily includes the spatial components A_i to ensure its gauge invariance under spatial gauge transformations. We derive the 1-loop effective action in the `electric' and `magnetic' sectors, summing up all powers of A_4.

RevTex4, 2 figures

References in corpus (5)

• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
• Heavy quark free energies and the renormalized Polyakov loop in full QCD
• The thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature
• Covariant derivative expansion of Yang-Mills effective action at high temperatures
• Covariant derivative expansion of fermionic effective action at high temperatures

Cited by in corpus (24)

• Susceptibilities and speed of sound from PNJL model
• Two-loop QCD gauge coupling at high temperatures
• Renormalized Polyakov loops in many representations
• Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials
• Effective Theory of Wilson Lines and Deconfinement
• Effective matrix model for deconfinement in pure gauge theories
• Confining ensemble of dyons
• Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model
• Fuzzy Bags and Wilson Lines
• Topology and confinement
• Deconfinement in Matrix Models about the Gross--Witten Point
• Small shear viscosity in the semi quark gluon plasma
• Baryon Inhomogeneity Generation in the Quark-Gluon Plasma Phase
• Collisional energy loss above the critical temperature in QCD
• Eigenvalue repulsion in an effective theory of SU(2) Wilson lines in three dimensions
• Strings with a confining core in a Quark-Gluon Plasma
• Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions
• Effects of quarks on the formation and evolution of Z(3) walls and strings in relativistic heavy-ion collisions
• Meson properties and phase diagrams in a SU(3) nlPNJL model with lQCD-inspired form factors
• Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters
• Determinant of the SU(N) caloron with nontrivial holonomy
• Effective Lagrangian for the Polyakov line on a lattice
• Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills
• Gluon condensate from the Polyakov loop