The phase structure of the two-flavor Polyakov-loop extended Nambu-Jona-Lashinio model is explored at finite temperature and imaginary chemical potential with a particular emphasis on the confinement-deconfinement transition. We point out that the confined phase is characterized by a $\cos3μ_I/T$ dependence of the chiral condensate on the imaginary chemical potential while in the deconfined phase this dependence is given by $\cosμ_I/T$ and accompanied by a cusp structure induced by the Z(3) transition. We demonstrate that the phase structure of the model strongly depends on the choice of the Polyakov loop potential $\mathcal{U}$. Furthermore, we find that by changing the four fermion coupling constant $G_s$, the location of the critical endpoint of the deconfinement transition can be moved into the real chemical potential region. We propose a new parameter characterizing the confinement-deconfinement transition.
The phase structure of Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model is explored at imaginary chemical potential, with particular emphasis on the deconfinement transition. We point out that the statistical confinement nature of the model naturally leads to characteristic dependence of the chiral condensate $<\bar{q}q>$ on $θ=μ_I/T$. We introduce a dual parameter for the deconfinement transition by making use of this dependence. By changing a four-fermion coupling constant, we tune the location of the critical endpoint of the deconfinement transition.
We investigate chiral and deconfinement transitions in the framework of the strong coupling lattice QCD for color SU(3) with one species of unrooted staggered fermion at finite temperature and quark chemical potential. We take account of the leading order Polyakov loop terms as well as the next-to-next-to-leading order (1/g^4) fermionic terms of the strong coupling expansion in the effective action. We investigate the Polyakov loop effects by comparing two approximation schemes, a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The ef…
The deconfinement transition in SU(2) gauge theory and the magnetization transition in the Ising model belong to the same universality class. The critical behaviour of the Ising model can be characterized either as spontaneous breaking of the Z_2 symmetry of spin states or as percolation of appropriately defined spin clusters. We show that deconfinement in SU(2) gauge theory can be specified as percolation of Polyakov loop clusters with Fortuin-Kasteleyn bond weights, leading to the same (Onsager) critical exponents as the conventional order-disorder description based on the Polyakov loop expe…
We show that recent available lattice data for the renormalized Polyakov loop above the deconfinement phase transition exhibit unequivocal inverse power temperature corrections driven by a dimension 2 gluon condensate. This simple ansatz provides a good overall description of the data throughout the deconfinement phase until near the critical temperature with just two parameters. One of the parameters is consistent with perturbation theory while a second, non perturbative, parameter provides a numerical value of the condensate which is close to existing zero and finite temperature determinatio…
The susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent of the renormalization of the Polyakov loop and only weakly dependent on the system size. The ratios are almost temperature independent above and below the transition and exhibit a discontinuity at the transition temperature. This characteristic behavior can be understood in terms of the global Z(3) symmetry of the Yang-Mills Lagrangian…
We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transition. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consid…
We use the Polyakov loop coupled quark-meson model to approximate low energy QCD and present results for the chiral and deconfinement transitions in the presence of a constant magnetic background $B$ at finite temperature $T$ and baryon chemical potential $μ_B$. We investigate effects of various gluoni potentials on the deconfinement transition with and without a fermionic backreaction at finite $B$. Additionally we investigate the effect of the Polyakov loop on the chiral phase transition, finding that magnetic catalysis at low $μ_B$ is present, but weakened by the Polyakov loop.
We explore the use of Wilson flow to study the deconfinement transition in SU(3) gauge theory. We use the flowed Polyakov loop as a renormalized order parameter for the transition, and use it to renormalize the Polyakov loop. We also study the flow properties of the electric and magnetic gluon condensates, and demonstrate that the difference of the flowed operators shows rapid change across the transition point.
The Polyakov loop is an order parameter to the confinement-deconfinement phase transition in pure gluodynamics. Recently a simple phenomenological model has been proposed to describe the available lattice data for the renormalized Polyakov loop in the deconfinement phase (hep-ph/0505215). These data exhibit unequivocal inverse power temperature corrections driven by a dimension two gluon condensate. The heavy quark free energy is also studied and compared to lattice data.
Using vector and axial-vector correlators within finite energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $Φ$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $μ$. The obtained results are in agreement with our initial conclusion, where we showed that $s_0(T,μ)$ and $Φ(T,μ)$ provide the same information for the QCD deconfinement transition.
We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $μ$ dependent scale, case III. In the cases I and II, at high chemical potential $μ$ and low temperature $T$ the main contribution to the free energy is due to th…
The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement-deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information…
We explore the thermodynamics and phase structure of the Polyakov loop-extended two flavor chiral quark--meson (PQM) model beyond the mean-field approximation at imaginary chemical potential. Our approach is based on the functional renormalization group (FRG) method. At finite temperature and imaginary chemical potential, we solve the renormalization group flow equation for a scale-dependent thermodynamic potential in the presence of the gluonic background field. We determine behavior of order parameters of the PQM model in the FRG approach and compute the phase diagram. We compare our FRG res…
In the heavy, static quark mass regime of QCD, the Polyakov loop is well known to be an order parameter of the deconfinement phase transition; however, the sensitivity of the Polyakov loop to the deconfinement of light, dynamical quarks is less clear. On the other hand, from the perspective of an effective Lagrangian written in the vicinity of the chiral transition, the Polyakov loop is an energy-like operator and should hence scale as any energy-like operator would. We show here that the Polyakov loop and heavy-quark free energy are sensitive to the chiral transition, i.e. their scaling is co…
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T-chi and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at T-chi is shown to be supported by finite temperature lattice calculations.
We extend the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model by introducing an effective four-quark vertex depending on Polyakov loop. The effective vertex generates entanglement interactions between Polyakov loop and chiral condensate. The new model is consistent with lattice QCD data at imaginary quark-number chemical potential and real and imaginary isospin chemical potentials, particularly on strong correlation between the chiral and deconfinement transitions and also on the quark-mass dependence of the order of the Roberge-Weiss endpoint predicted by lattice QCD very lately. We in…
We study the relation between the continuum threshold as function of the temperature $s_0(T)$ within finite energy sum rules and the trace of the Polyakov loop $Φ$ in the framework of a nonlocal SU(2) chiral quark model, establishing a contact between both deconfinement order parameters at finite temperature $T$ and chemical potential $μ$. In our analysis, we also include the order parameter for the chiral symmetry restoration, the chiral quark condensate. We found that $s_0$ and $Φ$ providing us the same information for the deconfinement transition, both for the zero and finite chemical poten…
Inhibition of splitting of the chiral and deconfinement transition due to rotation in QCD: the phase diagram of linear sigma model coupled to Polyakov loop
A synthesis of Polyakov loop models of the deconfinement transition and quasiparticle models of gluon plasma thermodynamics leads to a class of models in which gluon quasiparticles move in a non-trivial Polyakov loop background. These models are successful candidates for explaining both critical behavior and the equation of state for the SU(3) gauge theory at temperatures above the deconfinement temperature T_c. Polyakov loops effects are most important at intermediate temperatures from T_c up to roughly 2.5 T_c, while quasiparticle mass effects provide the dominant correction to blackbody beh…
I discuss the deconfinement transition in 2+1 flavor QCD in terms of Polyakov loops as well as the hadron resonance gas for hadrons containing static quarks and charm quarks.
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${\mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${\mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the…
We study interplay between confinement/deconfinement and chiral properties. We derive some analytical relations of the Dirac modes with the confinement quantities, such as the Polyakov loop, its susceptibility and the string tension. For the confinement quantities, the low-lying Dirac eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. This indicates no direct, one-to-one correspondence between confinement/deconfinement and chiral properties in QCD. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clove…
We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows and the first-order transition ends in a critical endpoint. The nature of the critical endpoint is examined by studying the longitudinal and transverse fluctuations of the Polyakov loop, quantified by the corresponding susceptibilities. The longitudinal susceptibility is enhanced in the critical region, while the transverse susceptibility show…
The behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0$ MeV the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electr…
We compare two order parameters for the deconfinement transition, induced by thermal and density effects, commonly used in the literature, namely the thermal and density evolution of the continuum threshold $s_{0}$, within the frame of the QCD sum rules, and the trace of the Polyakov loop $Φ$ in the framework of a nonlocal $SU(2)$ chiral quark model. We include in our discussion the evolution of the chiral quark condensate, the parameter that characterizes the chiral symmetry restoration. We found that essentially both order parameters, $s_{0}$ and $Φ$, provide the same information for the dec…
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature $T_χ$ and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behavior of Polyakov loop susceptibilities at $T_χ$ is shown to be supported by finite temperature lattice calculations.
The Polyakov loop potential serves to distinguish between the confined hadronic and the deconfined quark-gluon plasma phases of QCD. For Nf=2+1 quark flavors with physical masses we determine the Polyakov loop potential at finite temperature and density and extract the location of the deconfinement transition. We find a cross-over at small values of the chemical potential running into a critical end-point at mu/T > 1.
Unquenching of the Polyakov-loop potential showed to be an important improvement for the description of the phase structure and thermodynamics of strongly-interacting matter at zero quark chemical potentials with Polyakov-loop extended chiral models. This work constitutes the first application of the quark backreaction on the Polyakov-loop potential at nonzero density. The observation is that it links the chiral and deconfinement phase transition also at small temperatures and large quark chemical potentials. The build up of the surface tension in the Polyakov-loop extended Quark-Meson model i…
A synthesis of Polyakov loop models of the deconfinement transition and quasiparticle models of gluon plasma thermodynamics leads to a class of models in which gluons move in a non-trivial Polyakov loop background. These models are successful candidates for explaining both critical behavior and the equation of state for the SU(3) gauge theory at finite temperature. Two sensitive lattice probes which can discriminate between models are the Polyakov loop P and e-3p.
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.
While the Polyakov loop is an order parameter of the deconfinement transition in the heavy quark mass regime of QCD, its sensitivity to the deconfinement of light, dynamical quarks in QCD is not apparent. On the other hand, the quark mass dependence of the Polyakov loop is sensitive to the appearance of a chiral phase transition. Using lattice QCD calculations in the staggered fermion discretization scheme at finite values of the lattice spacing, $aT = 1/8$, we show here, for the first time, that the Polyakov loop expectation value, and the heavy quark free energy extracted from it, behave lik…
We present unambiguous evidence from lattice simulations of QCD with three degenerate quark species for two tricritical points in the (T,m) phase diagram at fixed imaginary μ/T=iπ/3 mod 2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary chemical potential, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. T…
In order to come closer to a realistic model of high-energy collisions, we simulate SU(2) lattice gauge theory under fluctuating temperature. The fluctuations are Euler-Gamma distributed, leading to a canonical state maximizing the Renyi and Tsallis entropy formulas. We test the random lattice spacing method numerically on the Polyakov Loop expectation value. The critical coupling and presumably also the critical deconfinement temperature shifts about 30 per cent to higher values with a realistic degree of fluctuations.
The Polyakov loop extended Nambu and Jona-Lasinio model (PNJL model) in a mean field framework shows astonishingly good agreement with lattice QCD calculations which needs to be better understood. The present work reports on further developments concerning both Polyakov loop and mesonic fluctuations beyond mean field approximation. Corrections beyond mean field are of special interest for the thermal expectation values of the Polyakov loop $Φ$ and its conjugate $Φ^*$, which differ once the quark chemical potential is non-zero. Mesonic fluctuations are also considered with emphasis on the role …
We calculated the chiral condensate and the dressed Polyakov loop in the space-time $R\times S^{3}$ and $R\times H^{3}$. The chiral condensate is the order parameter for the chiral phase transition, and the dressed Polyakov loop is the order parameter for the deconfinement phase transition. When there is a current mass, critical points for the chiral and deconfinement phase transitions are different in the crossover region. We show that the difference is changed by the gravitational effect.
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
Effects of a uniform (electro-) magnetic background field are investigated in the two-flavor nonlocal Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Temperature-dependences of the chiral order-parameter and the Polyakov-loop are investigated under the magnetic field. In the nonlocal PNJL model with four-dimensional momentum dependent distribution function, pseudo-critical temperatures of the chiral and deconfinement transitions are coincident each other even if the magnetic field is strong. It means that we can check the reliability of the distribution function under the strong magne…
By using the dressed Polyakov loop or dual chiral condensate as an equivalent order parameter of the deconfinement phase transition, we investigate the relation between the chiral and deconfinement phase transitions at finite temperature and density in the framework of three-flavor Nambu--Jona-Lasinio (NJL) model. 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 $(T,μ)$ plane. In the case of explicit chiral symmetry breaking, it is found that the phase transitions are flavor dependent. For e…
I compute the deconfinement order parameter for the SU(2) lattice gauge theory, the Polyakov loop, using the fixed scale approach for two different scales and show how one can obtain a physical, renormalized, order parameter. The generalization to other gauge theories, including quenched or full QCD, is straightforward.
We investigate the rapid rise of the dressed Polyakov loop in the Nambu--Jona-Lasinio (NJL) model as a function of temperature. In QCD such a behaviour is interpreted as a confinement- deconfinement phase transition. However, we demonstrate that in the NJL model this is simply a remnant of the chiral transition.
The dual superconductivity is a promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture for SU(3) Yang-Mills theory, and showed the restricted field dominance (called conventionally Abelian dominance), and non-Abelian magnetic monopole dominance in the string tension. We have further demonstrated by measuring the chromoelectric flux that the non-Abelian dual Meissner effect exists and determined that the dual superconductivity for SU(3) case is of type I, which is in sharp contrast to the SU(2) case: the border of type I and type II. In this t…
We present a study of the free energy of parameterized Polyakov loops P in SU(2) and SU(3) lattice gauge theory as a function of the parameters that characterize P. We explore temperatures below and above the deconfinement transition, and for our highest temperatures T > 5 T_c we compare the free energy to perturbative results.
The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure o…
Ab initio numerical simulations of the thermodynamics of dense quark matter remain a challenge. Apart from the infamous sign problem, lattice methods have to deal with finite volume and discretization effects as well as with the necessity to introduce sources for symmetry-breaking order parameters. We study these artifacts in the Polyakov-loop-extended Nambu-Jona-Lasinio model, and compare its predictions to existing lattice data for cold and dense two-color matter with two flavors of Wilson quarks. To achieve even qualitative agreement with lattice data requires the introduction of two novel …
The deconfinement and chiral phase transitions are studied in the context of the electrized quark matter at finite temperature in the two-flavor Polyakov-Nambu--Jona-Lasinio model. Using the mean field approximation and an electric field independet regularization we show that the effect of temperature and/or electric fields is to partially restore the chiral symmetry. The deconfinement phase transition is slightly affected by the magnitude of the electric field. To this end we show how the effective quark masses and the expectation value of the Polyakov Loop are affected by the electric fields…
We review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.
We study the features of nonlocal SU(3) chiral quark models with wave function renormalization. Model parameters are determined from meson phenomenology, considering different nonlocal form factor shapes. In this context we analyze the characteristics of the deconfinement and chiral restoration transitions at finite temperature, introducing the couplings of fermions to the Polyakov loop. We analyze the results obtained for various thermodynamical quantities considering different Polyakov loop potentials and nonlocal form factors, in comparison with data obtained from lattice QCD calculations.
We report preliminary results on the chiral and deconfinement aspects of the QCD transition at finite temperature using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent of N_τ=6 and 8. The chiral aspects of the transition are studied in terms of quark condensates and the disconnected chiral susceptibility. We study the deconfinement transition in terms of the strange quark number susceptibility and the renormalized Polyakov loop. We made continuum estimates for some quantities and find reasonably good agreement between our results and the recent continuum extr…
Dual meson condensates as possible order parameters for deconfinement are investigated in a Polyakov-loop enhanced linear sigma model of QCD at both zero and finite isospin chemical potential $μ_I$. We find that the rapid rise of the dual sigma condensate (corresponding to the dressed Polyakov-loop) with $T$ is driven by the chiral transition, no matter whether the Polyakov-loop dynamics is included or not. For $μ_I>m_π/2$, the dual sigma condensate shows abnormal thermal behavior which even decreases with $T$ below the melting temperature $T_c^{I_3}$ of pion superfluidity; On the other hand, …
We study the deconfinement and chiral restoration transitions in the context of non-local PNJL models, considering the impact of the presence of dynamical quarks on the scale parameter appearing in the Polyakov potential. We show that the corresponding critical temperatures are naturally entangled for both zero and imaginary chemical potential, in good agreement with lattice QCD results. We also analyze the Roberge Weiss transition, which is found to be first order at the associated endpoint.
The phase transitions characterized by deconfinement and restoration of chiral symmetry as well as the restoration of axial symmetry, at finite temperature, are investigated in the framework of SU(2) Polyakov-Nambu-Jona-Lasinio (PNJL) models with the U$_A$(1) anomaly. The thermodynamics of the phase transitions, the topological susceptibility, the meson spectrum, and, in particular, the convergence of axial and chiral partners are analyzed, in the framework of the ordinary PNJL model and in its extension, the entangled Polyakov-Nambu-Jona-Lasinio (EPNJL) model. The latter incorporates entangle…
We investigate the confinement-deconfinement transition at finite temperature in terms of the probability distribution of Polyakov-loop complex-phase via the Jensen-Shannon divergence. The Jensen-Shannon divergence quantifies the difference of two probability distributions, namely the target and reference probability distributions. We adopt the complex-phase distributions of the spatially averaged Polyakov loop at $μ/T=0$ and $μ/T=iπ/3$ as the target and reference distributions, respectively. It is shown that the Jensen-Shannon divergence has the inflection point when the target system approac…
In the Nambu--Jona-Lasinio model with Polyakov loops, we explore the relation between the deconfinement and chiral phase transitions within the mean-field approximation. We focus on the phase structure of the model and study the susceptibilities associated with corresponding order parameters.
