Dynamics and thermodynamics of a nonlocal Polyakov--Nambu--Jona-Lasinio   model with running coupling
  A nonlocal covariant extension of the two-flavor Nambu and Jona-Lasinio (NJL) model is constructed, with built-in constraints from the running coupling of QCD at high-momentum and instanton physics at low-momentum scales. Chiral low-energy theorems and basic current algebra relations involving pion properties are shown to be reproduced. The momentum-dependent dynamical quark mass derived from this approach is in agreement with results from Dyson-Schwinger equations and lattice QCD. At finite temperature, inclusion of the Polyakov loop and its gauge invariant coupling to quarks reproduces the dynamical entanglement of the chiral and deconfinement crossover transitions as in the (local) PNJL model, but now without the requirement of introducing an artificial momentum cutoff. Steps beyond the mean-field approximation are made including mesonic correlations through quark-antiquark ring summations. Various quantities of interest (pressure, energy density, speed of sound etc.) are calculated and discussed in comparison with lattice QCD thermodynamics at zero chemical potential. The extension to finite quark chemical potential and the phase diagram in the $(T,\mu)$-plane are also discussed. 
T. Hell, S. Roessner, M. Cristoforetti, and W. Weise