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

The dual quark condensate ${\mathrm{\Sigma }}^{(n)}$ 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 model, where $n$ are winding numbers. The Polyakov-loop extended Nambu–Jona-Lasinio model well reproduces lattice QCD data on ${\mathrm{\Sigma }}^{(1)}$ measured very lately. The dual quark condensate ${\mathrm{\Sigma }}^{(n)}$ 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.