Renormalized Polyakov loops in many representations

Abstract

We present a renormalization procedure for Polyakov loops which explicitly implements the fact that the renormalization constant depends only on the ultraviolet cutoff. Using this we study the renormalized Polyakov loops in all representations upto the {\bf 27} of the gauge group SU(3). We find good evidence for Casimir scaling of the Polyakov loops and for approximate large-N factorization. By studying many loops together, we are able to show that there is a matrix model with a single coupling which can describe the high temperature phase of QCD, although it is hard to construct explicitly. We present the first results for the non-vanishing renormalized octet loop in the thermodynamic limit below the SU(3) phase transition, and estimate the associated string breaking distance and the gluelump binding energy. By studying the connection of the direct renormalization procedure with a generalization of an earlier suggestion which goes by the name of the $Q\bar{Q}$ renormalization procedure, we find that they are functionally equivalent.

17 pages, 24 figures, revtex4

References in corpus (3)

• The Phase Structure of the Polyakov--Quark-Meson Model
• The Polyakov Loop and its Relation to Static Quark Potentials and Free Energies
• A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions

Cited by in corpus (8)

• Suppression of the Shear Viscosity in a "semi" Quark Gluon Plasma
• Renormalized Polyakov Loop in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Casimir scaling in G(2) lattice gauge theory
• Zero Point Energy of Renormalized Wilson Loops
• Heavy quark free energies for three quark systems at finite temperature
• Thermalization in SU(3) gauge theory after a deconfining quench
• Phases and properties of quark matter
• Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills