Dual quark condensate in the Polyakov-loop extended Nambu–Jona-Lasinio model

Abstract

The dual quark condensate ${\ensuremath{\Sigma}}^{(n)}$ proposed recently as a new order parameter of the spontaneous breaking of the ${\mathbb{Z}}_{3}$ symmetry are evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model, where $n$ are winding numbers. The Polyakov-loop extended Nambu--Jona-Lasinio model well reproduces lattice QCD data on ${\ensuremath{\Sigma}}^{(1)}$ measured very lately. The dual quark condensate ${\ensuremath{\Sigma}}^{(n)}$ at higher temperatures is sensitive to the strength of the vector-type four-quark interaction in the Polyakov-loop extended Nambu--Jona-Lasinio model and hence a good quantity to determine the strength.