Induced Chern-Simons term in lattice QCD at finite temperature

The general conditions for the Chem-Simons action to be induced as a non-universal contribution of fermionic determinant are formulated in finite-temperature lattice QCD. The dependence of the corresponding coefficient in the action on non-universal parameters (chemical potentials, vacuum features, etc.) is explored. Special attention is paid to the role of A₀-condensate if it is available in this theory.     

Universality in finite temperature lattice QCD

In the lattice regularization of QCD, physical results must be independent of the choice of lattice action. Finite temperature thermodynamics provides a very sensitive test of this universality, providing a functional comparison between the predictions of different actions. We study thermodynamics using Wilson's, Manton's and Villain's actions as well as the mixed fundamental-adjoint form of Bhanot and Creutz. Our results support universality in all cases, but indicate that in general the region of couplings in present lattice calculations requires the inclusion of higher order effects in the perturbative solution of the renormalization group equation.     

Interquark potential with finite quark mass from lattice QCD

We present an investigation of the interquark potential determined from the q ?q Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q ?q potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schr?dinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a≈2.1 GeV in a range 1.0≤m(q)≤3.6 GeV. Our numerical results show that the q ?q potential in the m(q)→∞ limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q ?q potential and the spin-spin potential are also examined.     

Incorporating dynamical light quarks in lattice QCD at finite temperature

Using the pseudo-fermion Monte Carlo method we investigate the chiral and the deconfinement phase transitions in the SU(3) gauge theory with dynamical staggered fermions on a 6³ × 2 lattice. The energy density of the gluonic sector ε_G, the average thermal Wilson loop |L| and the order parameter are found to have a rapid variation in the same range of β (=6/g²). The variation is similar to that observed in the quenched theory but is at a smaller value of β.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

A lattice test of strong coupling behaviour in QCD at finite temperature

We propose a set of lattice measurements which could test whether the deconfined, quark–gluon plasma, phase of QCD shows strong coupling aspects at temperatures a few times the critical temperature for deconfinement. The measurements refer to twist-two operators which are not protected by symmetries and which in a strong-coupling scenario would develop large, negative, anomalous dimensions, resulting in a strong suppression of the respective lattice expectation values in the continuum limit. Special emphasis is put on the twist-two operator with lowest spin (the spin-2 operator orthogonal to the energy–momentum tensor within the renormalization flow) and on the case of quenched QCD, where this operator is known for arbitrary values of the coupling: this is the quark energy–momentum tensor. The proposed lattice measurements could also test whether the plasma constituents are pointlike (as expected at weak coupling), or not.     

Determination of the renormalized heavy-quark mass in lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte Carlo data on a small 8³ × 16 lattice for β = 6. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit both the short-distance part and long-distance part of the correlator in such a small volume.     

Constituent quark screening lengths in finite temperature lattice QCD

Landau gauge quark propagators are calculated in both the confined and the deconfined phases of QCD. We discuss the magnitude of the resulting screening lengths as well as aspects of chiral symmetry relevant to the quark propagator.     

Phase transition in finite density and temperature lattice QCD

We investigate the behavior of the chiral condensate in lattice QCD at finite temperature and finite chemical potential. The study was done using two flavors of light quarks and with a series of β and ma at the lattice size 24×12²×6. The calculation was done in the Taylor expansion formalism. We are able to calculate the first and second order derivatives of <ψψ> in both isoscalar and isovector channels. With the first derivatives being small, we find that the second derivatives are sizable close to the phase transition and that the magnitude of ψψ decreases under the influence of finite chemical potential in both channels.     

QCD sum rules at finite temperature

Finite energy and Laplace transform QCD sum rules atT0 are analyzed, and predictions for vacuum condensates are compared with the low temperature expansion of the energy density and pressure. Results show a serious disagreement which indicates a breakdown of the FESR programme already at dimension four, and which invalidates Laplace transform sum rules, at least in their straightforward extension to finite temperature.     

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.     

The effective QCD lagrangian at finite temperature

We evaluate the one-loop effective potential at finite temperature for QCD. High-temperature as well as low-temperature limits are investigated. We do not find a phase transition, i.e., the asymmetric Copenhagen ground state is maintained for any temperature.     

Nonperturbative phenomena in QCD at finite temperature

The main objective of the present study is to analyze various nonperturbative phenomena in QCD both at low, T < T _c , and at high, T > T _c , temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCD on a lattice and, on the other hand, to study new physical phenomena in QCD at finite temperature.     

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.