Chiral condensate and dressed Polyakov loop in the Nambu--Jona-Lasinio model

Abstract

We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in two-flavor Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of dressed Polyakov loop in absence of any confinement mechanism is quite interesting, with only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\mu )$ plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration $T_c^{\chi }$ is smaller than that of the dressed Polyakov loop $T_c^{\mathcal{D}}$ in the low baryon density region where the transition is a crossover. With the increase of current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of $T_c^{\chi }=T_c^{\mathcal{D}}$ in the case of 1st and 2nd order phase transitions, and $T_c^{\chi }<T_c^{\mathcal{D}}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored but the color degrees of freedom are still confined.

7 pages, 10 figures

References in corpus (22)

• Color superconductivity in dense quark matter
• The QCD transition temperature: results with physical masses in the continuum limit
• The QCD transition temperature: results with physical masses in the continuum limit II.
• The Phase Structure of the Polyakov--Quark-Meson Model
• The transition temperature in QCD
• Thermodynamics of the QCD plasma and the large-N limit
• Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops
• Susceptibilities and speed of sound from PNJL model
• Two lectures on color superconductivity
• 2+1 Flavor Polyakov--Nambu--Jona-Lasinio Model at Finite Temperature and Nonzero Chemical Potential
• Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Dual quark condensate and dressed Polyakov loops
• Chiral and deconfinement transition from Dyson-Schwinger equations
• Linking confinement to spectral properties of the Dirac operator
• The NJL model of dense three-flavor matter with axial anomaly: the low temperature critical point and BEC-BCS diquark crossover
• Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
• Spectral sums of the Dirac-Wilson Operator and their relation to the Polyakov loop
• Complete spectra of the Dirac operator and their relation to confinement
• Relation between chiral symmetry breaking and confinement in YM-theories
• Dual quark condensate in the Polyakov-loop extended Nambu--Jona-Lasinio model
• Correlations among discontinuities in QCD phase diagram

Cited by in corpus (22)

• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field
• Is f0(1710) a glueball?
• Nonlocal PNJL model beyond mean field and the QCD phase transition
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Wess-Zumino-Witten action and photons from the Chiral Magnetic Effect
• Nonlocal Polyakov-Nambu-Jona-Lasinio model and imaginary chemical potential
• Quark Matter in a Strong Magnetic Background
• Probing deconfinement in a chiral effective model with Polyakov loop at imaginary chemical potential
• Inverse magnetic catalysis and confinement within a contact interaction model for quarks
• Thermodynamic potential with correct asymptotics for PNJL model
• Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD
• Dressed Polyakov loop and flavor dependent phase transitions
• Quark Number Susceptibility : Revisited with Fluctuation-Dissipation Theorem in mean field theories
• Dual Fermion Condensates in Curved Space
• Physical interpretation of the dressed Polyakov loop in the Nambu--Jona-Lasinio model
• Deconfinement transition and Black Holes
• Dual condensates at finite isospin chemical potential
• Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potential
• Dual meson condensates in the Polyakov-loop extended linear sigma model
• Thermo-magnetic nonlocal NJL model in the real and imaginary time formalisms
• Late-Time Cosmic Acceleration from QCD Confinement Dynamics