Mean-field QCD model for hot/dense matter

Perturbative estimates of thermodynamical quantities relevant for ultra-relativistic collisions of heavy nuclei are found unreliable and some recent effective models for hot and dense QCD matter are found to have very little in common with QCD. A mean-field model, resembling QCD and yielding qualitatively correct results, is suggested and discussed.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

The dynamical holographic QCD method for hadron physics and QCD matter

In this paper we present a short overview on the dynamical holographic QCD (DhQCD) method for hadron physics and QCD matter. The five-dimensional DhQCD model is constructed in the graviton-dilaton-scalar framework with the dilaton background field Φ and the scalar field X dual to the gluon condensate and the chiral condensate operator thus can represent the gluodynamics (linear confinement) and chiral dynamics (chiral symmetry breaking), respectively. The dilaton background field and the scalar field are a function of the 5th dimension, which plays the role of the energy scale, in this way, the DhQCD model can resemble the renormalization group from ultraviolet (UV) to infrared (IR). By solving the Einstein equation, the metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. We review the results on the hadron spectra including the glueball spectra, the light/heavy meson spectra, as well as on QCD phase transitions, and thermodynamical as well as transport properties in the framework of the DhQCD model.     

QCD and a holographic model of hadrons

We propose a five-dimensional framework for modeling low-energy properties of QCD. In the simplest three parameter model we compute masses, decay rates and couplings of the lightest mesons. The model fits experimental data to within 10%. The framework is a holographic version of the QCD sum rules, motivated by the anti-de Sitter/conformal field theory correspondence. The model naturally incorporates properties of QCD dictated by chiral symmetry, which we demonstrate by deriving the Gell-Mann-Oakes-Renner relationship for the pion mass.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

High statistics study of the chiral condensate in quenched lattice QCD

We present the results of a high statistics study of the chiral condensate in quenched lattice QCD on an 8⁴ lattice at β = 5.4, 5.5, 5.6, 5.7, 5.8 and 6.0. We see clear evidence for deviation from asymptotic scaling in the range of β considered. Our results are in agreement with the behaviour anticipated from recent Monte Carlo renormalisation group studies of the β-function. We find indications of a common scaling behaviour for the condensate, the string tension and the deconfinement temperature.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential , for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for . The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1. Received: 20 June 2000 / Published online: 31 August 2000     

Criticality of QCD in a holographic QCD model with critical end point

The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in T-μ plane qualitatively. Critical exponents along different axes(α,β,γ,δ) are extracted numerically. It is given that α≈0,β≈0.54,γ≈1.04, and δ≈2.97,which is similar to the three-dimensional Ising mean-field approximation and previous holographic QCD model calculations. We also discuss the possibilities to go beyond the mean field approximation by including the full back-reaction of the chiral dynamics in the holographic framework.     

Some remarks on chiral symmetry in dense matter

The restoration of chiral symmetry in quantum chromodynamics as the temperatureT and the chemical potential |μ| are increased is discussed qualitatively and using effective field theories. The latter are shown not to give reliable quantitative estimates. It is argued that a dilute gas of instantons cannot be the main dynamical agent responsible for the breakdown of chiral symmetry.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

A color magnetic vortex condensate in QCD

It is shown that there exists a very close analogy between a lattice of vortices in a superconductor near the critical field and a condensate of color magnetic flux tubes due to the unstable mode in QCD. This analogy makes it possible to identify a dynamical Higgs field in QCD. We show that the color magnetic flux tubes are quantized in terms of the center group Z(2) in the SU(2) case. In the case of SU(N) it is possible to select a color direction of the field such that one has Z(N) quantization.     

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.     

Hadrons in dense QCD

The theoretical foundation of the in-medium hadron properties is discussed from the point of view of the QCD spectral functions. The dynamical models of in-medium hadrons proposed so far are also summarized.