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We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $mu_5$, increases. The two crossovers are reasonably close to each other in the range of $mu_5$ examined here and the pseudocritical temperatures rise with $mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $kappa_5 simeq - 0.011$. We point out that the presence of $mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.
Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD, which severely limits our understanding of the QCD phase diagram. In this review I collect results for the phase structure in an extended parameter space of
The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, mu_B and mu_{iso}, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type ei
The confinement-deconfinement transition is discussed from topological viewpoints. The topological change of the system is achieved by introducing the dimensionless imaginary chemical potential ($theta$). Then, the non-trivial free-energy degeneracy
We have computed the chiral susceptibility in quark-gluon plasma in presence of finite chemical potential and weak magnetic field within hard thermal loop approximation. First we construct the massive effective quark propagator in a thermomagnetic me
We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark