I review recent results obtained within chiral effective models, on the phase structure of hot quark matter in a strong magnetic background. After a brief introduction, I focus on the results obtained within two chiral models improved with the Polyakov loop. The models differ for the content of interactions, but both of them are tuned to reproduce Lattice QCD thermodynamics at zero and imaginary chemical potential. One of them takes into account an explicit Polyakov loop dependence of the coupling; the other one neglects this contribution, but takes into account multi-quark interactions. A comparison between the phase diagrams of the two models is presented.
Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and $\textit{d}$-wave superconducting ($\textit{d}$SC) phases, the influences of gauge boson mass $m_{a}$ on chiral symmetry restoration and deconfinement phase transitions in QED$_{3}$ are investigated simultaneously within a unified framework, i.e., Dyson-Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass $m_{a}$ is a typical second-order phase transition; the chiral symmetry restoration and deconfinement p…
The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions under magnetic fields is investigated in a Pauli-Villars regularized PNJL model. A linear-in-$B$ term for quark anomalous magnetic moment is introduced to the Lagrangian density of our model, and it plays the role of inverse catalysis to the phase transitions. With fixed magnetic field, the critical temperature decreases with quark AMM. When fixing quark AMM, the critical temperature increases with magnetic field for a small quark AMM, but decreases with magnetic field for a large quar…
Deconfinement and chiral restoration within the SU(3) Polyakov--Nambu--Jona-Lasinio and entangled Polyakov--Nambu--Jona-Lasinio models in an external magnetic field
The Doctoral thesis of William Naylor. Gives the background of the three papers included, specifically introducing both the quark meson model and the NJL model, the basic formalism of thermal field theory, and functional renormalization group (including some details on numerically solving the FRG equation for the QM model).
Paradigme shift in gauge topology, from instantons to their constituents -- instanton-dyons -- has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high density explains the chiral symmetry breaking. Unlike instantons, these objects have electric and magnetic charges. Their back reaction on the mean value of the Polyakov line (holonomy) allows to explain the deconfinement transition. The talk summarizes recent works on the dyon ensemble, done in the mean field approximation (MFA), and also by direct numerica…
For studies of quark matter in astrophysical scenarios the thermodynamic bag model (tdBag) is commonly employed. Although successful, it does not account for dynamical chiral symmetry breaking (D$χ$SB) and repulsions due to the vector interaction which is crucial to explain recent observations of massive, two solar mass neutron stars. In Klähn & Fischer (2015) we developed the novel vBag quark matter model which takes these effects into account. This article extends vBag to finite temperatures and isospin asymmetry. Another particular feature of vBag is the determination of the deconfinement b…
In this paper, the deconfinement and chiral restoration transitions in strong magnetic field is realized at zero temperature in the Polyakov Nambu$-$Jona-Lasinio model. We provide the thermodynamic treatment to mimic the deconfinement phase transition at zero temperature together with the entangled scalar and vector interactions coupled with the Polyakov loop. The magnetic catalysis is found by a rising behavior of the critical chemical potential for the first-order deconfinement phase transition. While the magnetic catalysis on the chiral restoration could convert to inverse magnetic catalysi…
The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(μ_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $μ_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $μ_B^c$ d…
We study the impact of steady, homogeneous, and external parallel electric and magnetic field strength ($eE\parallel eB$), on the chiral symmetry breaking-restoration and confinement-deconfinement phase transitions. We also sketch the phase diagram of quantum chromodynamics (QCD) at finite temperature $T$ and in the presence of background fields. Our unified formalism for this study is based on the Schwinger-Dyson equations, symmetry preserving vector-vector contact interaction model of quarks, and the proper time regularization scheme. At $T=0$, in the purely magnetic case ($eE\rightarrow 0$)…
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…
I discuss the masses of chiral partners in the context of chiral symmetry restoration at finite temperature. Using the Nambu-Jona-Lasinio model I first remind the usual situation where two mesons of opposed parity become degenerate above the chiral transition temperature. Then I consider an effective theory for D mesons where the positive parity companion presents a "double pole structure". In this case three different masses need to be analyzed as functions of the temperature. I suggest a possible restoration pattern at high temperatures when the back-reaction of the quark condensate is incor…
We discuss recent results regarding the interplay between chiral and $U(1)_A$ symmetry restoration, both from the point of view of Ward Identities relating meson susceptibilities and quark condensates, and from the behaviour of light meson resonances at finite temperature
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…
