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Register a new userTriality in QCD at Zero and Finite Temperature: A New Direction
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Discrete symmetries in grand canonical ensembles and in ensembles canonical with respect to triality are investigated. We speculate about the general phase structure of finite temperature gauge theories with discrete $Z(N)$ symmetry. Low and high temperature phases turn out to be different in both ensembles even for infinite systems. It is argued that gauge theories with matter fields in the fundamental representation should be treated in ensembles canonical with respect to triality if one wants to avoid unphysical predictions. Further, we discuss as a physical consequence of such a treatment the impossibility of the existence of metastable phases in the quark-gluon plasma.
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I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector a vacuum wave functional is used which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170 MeV and 198 MeV, respectively, are obtained.
The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $mu_5$, increases. The two crossovers are reasonably close to each other in the range of $mu_5$ examined here and the pseudocritical temperatures rise with $mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $kappa_5 simeq - 0.011$. We point out that the presence of $mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.
The confinement-deconfinement transition is discussed from topological viewpoints. The topological change of the system is achieved by introducing the dimensionless imaginary chemical potential ($theta$). Then, the non-trivial free-energy degeneracy becomes the signal of the deconfinement transition and it can be visualized by using the map of the thermodynamic quantities to the circle $S^1$ along $theta$. To understand this topological deconfinement transition at finite real quark chemical potential ($mu_mathrm{R}$), we consider the isospin chemical potential ($mu_mathrm{iso}$) in the effective model of QCD. The phase diagram at finite $mu_mathrm{iso}$ is identical with that at finite $mu_mathrm{R}$ outside of the pion-condensed phase at least in the large-$N_mathrm{c}$ limit via the well-known orbifold equivalence. In the present effective model, the topological deconfinement transition does not show a significant dependence on $mu_mathrm{iso}$ and then we can expect that this tendency also appears at small $mu_mathrm{R}$. Also, the chiral transition and the topological deconfinement transition seems to be weakly correlated. If we will access lattice QCD data for the temperature dependence of the quark number density at finite $mu_mathrm{iso}$ with $theta=pi/3$, our surmise can be judged.
The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, mu_B and mu_{iso}, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type eight-quark interaction can reproduce lattice QCD data at not only mu_{iso}=mu_B=0 but also mu_{iso}>0 and mu_B=0. In the mu_{iso}-mu_{B}-T space, where T is temperature, the critical endpoint of the chiral phase transition in the mu_B-T plane at mu_{iso}=0 moves to the tricritical point of the pion-superfluidity phase transition in the mu_{iso}-T plane at mu_B=0 as mu_{iso} increases. The thermodynamics at small T is controlled by sqrt{sigma^2+pi^2} defined by the chiral and pion condensates, sigma and pi.
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