The QCD phase structure at high baryon density

We consider the possibility that color deconfinement and chiral symmetry restoration do not coincide in dense baryonic matter at low temperature. As a consequence, a state of massive “constituent” quarks would exist as an intermediate phase between confined nuclear matter and the plasma of deconfined massless quarks and gluons. We discuss the properties of this state and its relation to the recently proposed quarkyonic matter.     

The phase diagram of QCD

Simple thermodynamic reasoning is used to argue that at temperatures of the order of a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma of more elementary constituents called quarks and gluons. A review is presented of what is known about the plasma phase both from theoretical calculations and from experiments involving the collisions of large atomic nuclei moving at relativistic speeds. Finally the behaviour of nuclear material under conditions of extreme density is considered, and possible exotic phenomena such as quark matter and colour superconductivity are discussed.     

Lattice QCD at finite temperature and density

QCD at finite temperature and density is becoming increasingly important for various experimental programmes, ranging from heavy ion physics to astro-particle physics. The non-perturbative nature of non-abelian quantum field theories at finite temperature leaves lattice QCD as the only tool by which we may hope to come to reliable predictions from first principles. This requires careful extrapolations to the thermodynamic, chiral and continuum limits in order to eliminate systematic effects introduced by the discretization procedure. After an introduction to lattice QCD at finite temperature and density, its possibilities and current systematic limitations, a review of present numerical results is given. In particular, plasma properties such as the equation of state, screening masses, static quark free energies and spectral functions are discussed, as well as the critical temperature and the QCD phase structure at zero and finite density.     

Lattice results on QCD at high temperature and non-zero baryon number density

Studies of QCD thermodynamics on the lattice now can be performed with an almost realistic quark mass spectrum and on quite large lattices. This will soon allow a controlled extrapolation to the continuum limit. We present recent results on the QCD equation of state, discuss deconfining and chiral symmetry restoring aspects of the QCD transition at vanishing chemical potential and show results on baryon number, electric charge and strangeness fluctuations. We briefly discuss the generic structure of Taylor expansion coefficients in the vicinity of the chiral phase transition and comment on the determination of the anticipated chiral critical point within the framework of Taylor expansions of the QCD partition function.     

Fluctuations and the QCD phase diagram

In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.     

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

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 chemical potential μ/T = iπ/3 mod2π/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 μ, 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. The generalization to nondegenerate and light quark masses is discussed.     

Thermodynamics and phase diagram of high temperature superconductors

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).     

AdS/QCD at finite density and temperature

We review some basics of AdS/QCD following a non-standard path and list a few results from AdS/QCD or holographic QCD. The non-standard path here is to use the analogy of the way one obtains an effective model of QCD like linear sigma model and the procedure to construct an AdS/QCD model based on the AdS/CFT dictionary.     

QCD at high baryon density in a random matrix model

A high-density diquark phase seems to be a generic feature of QCD. If so it should also be reproduced by random matrix models. We discuss a specific one in which the random matrix elements of the Dirac operator are supplemented by a finite chemical potential and by non-random elements which model the formation of instanton-anti-instanton molecules. Comparing our results to those found in a previous investigation by Vanderheyden and Jackson we find additional support for our starting assumption, namely that the existence of a high-density diquark phase is common to all QCD-like model. Received: 20 February 2001 / Accepted: 24 April 2001     

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors \begin{document}$ N_f $\end{document} and colors \begin{document}$ N_c $\end{document} using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed \begin{document}$ N_f = 2 $\end{document} and varying \begin{document}$ N_c $\end{document}, we observe that the dynamical chiral symmetry is broken when \begin{document}$ N_c $\end{document} exceeds its critical value \begin{document}$ N^{c}_{c}\approx2.2 $\end{document}. For a fixed \begin{document}$ N_c = 3 $\end{document} and varying \begin{document}$ N_f $\end{document}, we observe that the dynamical chiral symmetry is restored when \begin{document}$ N_f $\end{document} reaches its critical value \begin{document}$ N^{c}_{f}\approx8 $\end{document}. Strong interplay is observed between \begin{document}$ N_c $\end{document} and \begin{document}$ N_f $\end{document}, i.e., larger values of \begin{document}$ N_c $\end{document} tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of \begin{document}$ N_f $\end{document} suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various \begin{document}$ N_c $\end{document} and \begin{document}$ N_f $\end{document}. At finite T and μ, we observe that the critical number of colors \begin{document}$ N^{c}_c $\end{document} is enhanced, whereas the critical number of flavors \begin{document}$ N^{c}_f $\end{document} is suppressed as T and μ increase. Consequently, the critical temperature \begin{document}$ T_c $\end{document}, \begin{document}$ \mu_c $\end{document}, and co-ordinates of the critical endpoint \begin{document}$ (T^{E}_c,\mu^{E}_c) $\end{document} in the QCD phase diagram are enhanced as \begin{document}$ N_c $\end{document} increases and suppressed when \begin{document}$ N_f $\end{document} increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.     

Finite size scaling on the phase diagram of QCD

In the last few years there has been remarkable progress in the comparison of experimental data on the shape of event-by-event distributions of conserved quantities and lattice thermodynamic predictions based on the grand canonical ensemble. In this talk we discuss how the QCD crossover temperature and the freezeout curve are extracted from the analysis of fluctuations. We report that one can also go further and locate the QCD critical point at ?? }~ 2T _c . We also list the systematics which must be brought under control in future.     

Lattice dynamics and phase diagram of aluminum at high temperatures

The dispersion of phonons in the fcc, hcp, and bcc phases of aluminum is calculated at ultrahigh pressures by the method of small displacements in a supercell. The stability of the phonon subsystem is studied. The thermodynamic characteristics are calculated in the quasi-harmonic approximation, and a phase diagram of aluminum is plotted. As compared to the Debye model, the use of a phonon spectrum calculated in the quasi-harmonic approximation significantly broadens the hcp phase field and strongly shifts the phase boundary between the fcc and bcc phases. The normal isentrope is calculated at megabar pressures. It is shown to intersect the fcc-hcp and hcp-bcc phase boundaries. The sound velocity along the normal isentrope is calculated. It is shown to have a nonmonotonic character.