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The present work generalizes a nonlocal version of the Polyakov loop-extendedNambu and Jona-Lasinio (PNJL) model to the case of three active quark flavors,with inclusion of the axial U(1) anomaly. Gluon dynamics is incorporatedthrough a gluonic background field, expressed in terms of the Polyakov loop.The thermodynamics of the nonlocal PNJL model accounts for both chiral anddeconfinement transitions. Our results obtained in mean-field approximation arecompared to lattice QCD results for $N_\text{f}=2+1$ quark flavors. Additionalpionic and kaonic contributions to the pressure are calculated in random phaseapproximation. Finally, this nonlocal 3-flavor PNJL model is applied to thefinite density region of the QCD phase diagram. It is confirmed that theexistence and location of a critical point in this phase diagram dependssensitively on the strength of the axial U(1) breaking interaction.

Thermodynamics of a three-flavor nonlocal Polyakov--Nambu--Jona-Lasinio model