Polyakov loop in chiral quark models at finite temperature

Abstract

We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.Comment: 24 pages, 8 ps figures. Figure and appendix added. To appear in Physical Review

Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop

“…[30,31]). In the present paper, we add the Polyakov loop to the model to include certain aspects of confinement [32,33]. In particular, we investigate a set of possible implementations of the Polyakov loop and how they effect both the chiral and deconfinement transitions.…”

Inhomogeneous chiral condensates

“…In order to mimic some features of confinement, in particular to suppress the contribution of free constituent quarks in the confined phase, and in order to include gluonic contributions to the pressure, the NJL model can be coupled to an effective description of the Polyakov loop [136,137,138,139]. The resulting model is known as the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model.…”

Meson fluctuations and thermodynamics of the Polyakov-loop-extended quark-meson model

“…Also, the physics of color deconfinement and its relation to chiral symmetry breaking has been recently studied in terms of effective chiral models [2][3][4][5][6][7][8][9][10][11][12][13]. The idea to extend the existing chiral models, such as the Nambu-JonaLasinio (NJL) or the chiral quark-meson model, by introducing couplings of quarks to uniform temporal background gauge fields (Polyakov loops) was an important step forward in these studies [5,13].…”