Renormalized Polyakov loops in many representations

TL;DR

This paper introduces a renormalization method for Polyakov loops in SU(3) gauge theory, demonstrating Casimir scaling, large-N factorization, and a matrix model for high-temperature QCD, with novel results on octet loops and string breaking.

Contribution

It develops a renormalization procedure for Polyakov loops that depends only on the ultraviolet cutoff and applies it to all representations up to 27, revealing new insights into QCD phase structure.

Findings

Evidence for Casimir scaling of Polyakov loops

Approximate large-N factorization observed

First results on non-vanishing octet loop below phase transition

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.