QCD Thermodynamics from the Lattice

We review the current methods and results of lattice simulations of quantum chromodynamics at nonzero temperatures and densities. The review is intended to introduce the subject to interested nonspecialists and beginners. It includes a brief overview of lattice gauge theory, a discussion of the determination of the crossover temperature, the QCD phase diagram at zero and nonzero densities, the equation of state, some in-medium properties of hadrons including charmonium, and some plasma transport coefficients.Comment: 74 pp. 31 figs. To appear in the European Physical Journal A and Advances in Physics of Particles and Nuclei. Added references, corrected typos, and updated the discussion of the thermal heavy quark/antiquark potential. Added and updated references. Final versio

Thermodynamics of the QCD plasma and the large-N limit

The equilibrium thermodynamic properties of the SU(N) plasma at finite temperature are studied non-perturbatively in the large-N limit, via lattice simulations. We present high-precision numerical results for the pressure, trace of the energy-momentum tensor, energy density and entropy density of SU(N) Yang-Mills theories with N=3, 4, 5, 6 and 8 colors, in a temperature range from 0.8T_c to 3.4T_c (where T_c denotes the critical deconfinement temperature). The results, normalized according to the number of gluons, show a very mild dependence on N, supporting the idea that the dynamics of the strongly-interacting QCD plasma could admit a description based on large-N models. We compare our numerical data with general expectations about the thermal behavior of the deconfined gluon plasma and with various theoretical descriptions, including, in particular, the improved holographic QCD model recently proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description for the QCD plasma in a phenomenologically interesting temperature range where the system, while still strongly-coupled, approaches a `quasi-conformal' regime characterized by approximate scale invariance. Finally, we perform an extrapolation of our results to the N to $\infty$ limit.Comment: 1+38 pages, 13 eps figures; v2: added reference

On Fluctuations of Conserved Charges : Lattice Results Versus Hadron Resonance Gas

We compare recent lattice results on fluctuations and correlations of strangeness, baryon number and electric charge obtained with p4 improved staggered action with the prediction of hadron resonance gas model. We show that hadron resonance gas can describe these fluctuations reasonably well if the hadron properties are as calculated on the lattice.Comment: 4 pages, LaTeX, uses jpconf.cls, to appear in the proceedings of 26th Winter Workshop on Nuclear Dynamic

Hot Quark Matter with an Axial Chemical Potential

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, $\mu_5$. The latter is introduced to mimic the chirality transitions induced, in hot Quantum Chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small $\mu_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line, and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.Comment: 12 pages, 7 figures. Few references added, short discussion included. Final version appearing on Phys. Rev.

Study of Charmonia near the deconfining transition on an anisotropic lattice with O(a) improved quark action

We study hadron properties near the deconfining transition in the quenched lattice QCD simulation. This paper focuses on the heavy quarkonium states, such as $J/\psi$ meson. In order to treat heavy quarks at $T>0$, we adopt the $O(a)$ improved Wilson action on anisotropic lattice. We discuss $c\bar{c}$ bound state observing the wave function and compare the meson correlators at above and below $T_c$. Although we find a large change of correlator near the $T_c$, the strong spatial correlation which is almost the same as confinement phase survives even $T\sim 1.5T_c$.Comment: 19 pages, 10 figure

The Instanton Molecule Liquid and "Sticky Molasses" Above T_c

The main objective of this work is to explore the evolution in the structure of the quark-antiquark bound states in going down in the chirally restored phase from the so-called "zero binding points" T_zb to the QCD critical temperature T_c at which the Nambu-Goldstone and Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by Shuryak and Zahed for charmed $\bar c c$, light-quark $\bar q q$ mesons $\pi, \sigma, \rho, A_1$ and gluons that at T_zb, the quark-antiquark scattering length goes through infinity at which conformal invariance is restored, thereby transforming the matter into a near perfect fluid behaving hydrodynamically, as found at RHIC. We show that the binding of these states is accomplished by the combination of (i) the color Coulomb interaction, (ii) the relativistic effects, and (iii) the interaction induced by the instanton-anti-instanton molecules. The spin-spin forces turned out to be small. While near T_zb all mesons are large-size nonrelativistic objects bound by Coulomb attraction, near T_c they get much more tightly bound, with many-body collective interactions becoming important and making the $\sigma$ and $\pi$ masses approach zero (in the chiral limit). The wave function at the origin grows strongly with binding, and the near-local four-Fermi interactions induced by the instanton molecules play an increasingly more important role as the temperature moves downward toward T_c.Comment: Contribution to QM2004 proceedings, 4 page