Polyakov loops, Gross-Witten like point and Hagedorn states

TL;DR

This paper investigates the phase transition behavior in a finite volume system with Polyakov loops using the PNJL model, revealing a Gross-Witten-like transition linked to Hagedorn states rather than traditional deconfinement.

Contribution

It introduces a novel interpretation of the phase transition as a Gross-Witten-like point associated with Hagedorn states, distinct from the standard deconfinement transition.

Findings

Polyakov loop signals a Gross-Witten-like transition instead of deconfinement.

Hagedorn states emerge as meta-stable states at the GW-like threshold.

Deconfinement occurs at Hagedorn temperature, above the GW-like point.

Abstract

The phase transition for a finite volume system that incorporates the Polyakov loops and maintains the colorless state is explored using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. The order parameter for Polyakov loops is demonstrated to signal the appearance of a transition for $SU(3)_{c}$ analogous to Gross-Witten (GW-) phase transition instead of the deconfinement phase transition to quark-gluon plasma. The asymptotic restoration of Polyakov loops is conjectured to be a threshold production for meta-stable Hagedorn (or semi-QGP) states and this does not imply a direct deconfinement phase transition. In this context, the GW-like point is the point where the colorless states switches from the low-lying hadronic states to the meta-stable high-lying Hagedorn states. The chiral phase transition takes place within an extended GW-like point depending on the fireball's size. The deconfinement phase transition is determined by Hagedorn's temperature above GW-like temperature.