We extend the Polyakov-loop improved Nambu–Jona-Lasinio model to $2+1$ flavor case to study the chiral and deconfinement transitions of strongly interacting matter at finite temperature and nonzero chemical potential. The Polyakov loop, the chiral susceptibility of light quarks ($u$ and $d$), and the strange quark number susceptibility as functions of temperature at zero chemical potential are determined and compared with the recent results of lattice QCD simulations. We find that there is always an inflection point in the curve of strange quark number susceptibility accompanying the appearance of the deconfinement phase, which is consistent with the result of lattice QCD simulations. Predictions for the case at nonzero chemical potential and finite temperature are made as well. We give the phase diagram in terms of the chemical potential and temperature and find that the critical end point moves down to low temperature and finally disappears with the decrease of the strength of the ’t Hooft flavor-mixing interaction.

We investigate both the chiral and deconfinement phase transitions of QCD matter in a refined scheme of Dyson-Schwinger equations, which have been shown to be successful in giving the meson mass spectrum and matching the interaction with the results from ab initio computation. We verify the equivalence of the chiral susceptibility criterion with different definitions for the susceptibility and confirm that the chiral susceptibility criterion is efficient to fix not only the chiral phase boundary but also the critical end point (CEP), especially when one could not have the effective thermodynamical potential. We propose a generalized Schwinger function criterion for the confinement. We give the phase diagram of both phase transitions and show that in the refined scheme the position of the CEP shifts to lower chemical potential and higher temperature. Based on our calculation and previous results of the chemical freeze-out conditions, we propose that the CEP is located in the states of the matter generated by the Au–Au collisions with $\sqrt{s_{NN}}=9–15\mathrm{GeV}$.

The gauge principle is fundamental in formulating the Standard Model. Fermion–gauge-boson couplings are the inescapable consequence and the primary determining factor for observable phenomena. Vertices describing such couplings are simple in perturbation theory and yet the existence of strong-interaction bound-states guarantees that many phenomena within the Model are nonperturbative. It is therefore crucial to understand how dynamics dresses the vertices and thereby fundamentally alters the appearance of fermion–gauge-boson interactions. We consider the coupling of a dressed-fermion to an Abelian gauge boson, and describe a unified treatment and solution of the familiar longitudinal Ward–Green–Takahashi identity and its less well known transverse counterparts. Novel consequences for the dressed-fermion–gauge-boson vertex are exposed.

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Maris-Tandy model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and fourth order fluctuations of net quark number all diverge at the critical endpoint (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the Maris-Tandy model and the Qin-Chang model, we give the pseudocritical temperature at zero quark chemical potential as $T_c=146\mathrm{MeV}$ and 150 MeV, and locate the CEP at $({\mu }_E^q,T_E)=(120,124)\mathrm{MeV}$ and (124,129) MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.

We introduce a novel method for computing the ($\mu$, $T$)-dependent pressure in continuum QCD, from which we obtain a complex phase diagram and predictions for thermal properties of the dressed-quark component of the system, providing the in-medium behavior of the related trace anomaly, speed of sound, latent heat, and heat capacity.