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.     

Nonperturbative QCD thermodynamics in the external magnetic field

The thermodynamics of quarks and gluons strongly depends on the vacuum colormagnetic field, which grows with the temperature T, so that spatial string tension \(\sigma _s =\mathrm{const}~ g^4 (T) T^2\). We investigate below what happens when one imposes in addition constant magnetic field and discover remarkable structure of the resulting thermodynamic potential.     

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.     

Low-energy theorems of QCD and bulk viscosity at finite temperature and baryon density in a magnetic field

The nonperturbative QCD vacuum at finite temperature and baryon density in an external magnetic field has been studied. Relations between the nonperturbative condensates and the thermodynamic pressure at T ≠ 0, μ _q ≠ 0, and H ≠ 0 have been obtained and the low-energy theorems have been derived. Bulk viscosity ζ(T, μ, H) has been described in terms of the main thermodynamic quantities characterizing the quark-gluon matter at T ≠ 0, μq ≠ 0, and H ≠ 0. Various limiting cases have been discussed.     

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.     

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.     

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.     

Nonperturbative expansion in QCD

The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β-function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.     

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.     

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.     

Singularity structure of massless QCD at finite temperature

A complete relativistic calculation to first order in the strong coupling constantα _s is presented for deep inelastic scattering of leptons off a heat bath of quarks and gluons. The singularity structure is studied and the cancellation of all collinear and infrared divergences is proven. It is shown that it is necessary to include all processes of a given order (i.e. not only the gluon emission and absorption as usually stated). We show that for non-equilibriumn _F andn _B distributions the collinear singularities do not cancel.     

Chiral symmetry breaking at finite temperature in Coulomb gauge QCD

Chiral symmetry breaking at finite temperature is analysed in Coulomb gauge QCD, using a suitably renormalised gap equation. In Coulomb gauge the gap equation is derived using the Ward identities and the Dyson equations for the vector and axial-vector vertices. Making the ladder approximation to the Bethe-Salpeter kernel relates the chiral symmetry breaking parameters to the static quark potential. It is thus possible to use a confining potential in the analysis of chiral symmetry breaking. We extend this to finite temperature. For a confining potential there is no chiral symmetry restoration at any finite temperature.     

Monte Carlo study of three-dimensional QCD at finite temperature

Three-dimensional QCD at finite temperature is analyzed using Monte Carlo calculations. It is shown that confinement at low temperature is lost through a second-order phase transition. At high temperature, static quarks are liberated and screened and it is argued that timelike (A₀) gluons are liberated. Just above the critical temperature electric correlation functions seem to be dominated by a resonance of two timelike gluons, whose existence is suggested by perturbation theory. The influence of an external magnetic field close to the critical point is considered.     

Complex heavy-quark potential at finite temperature from lattice QCD

We calculate for the first time the complex potential between a heavy quark and antiquark at finite temperature across the deconfinement transition in lattice QCD. The real and imaginary part of the potential at each separation distance r is obtained from the spectral function of the thermal Wilson loop. We confirm the existence of an imaginary part above the critical temperature T(C), which grows as a function of r and underscores the importance of collisions with the gluonic environment for the melting of heavy quarkonia in the quark-gluon plasma.     

Lattice QCD at finite temperature: A status report

We analyze the status of numerical simulation of QCD at finite temperature. Emphasis is put on quantitative predictions emerging from lattice calculations that may be tested in heavy ion experiments. Recent results on the chiral phase transition, thermodynamics of the quark gluon plasma phase and various screening lengths are discussed.     

Nonperturbative dynamics in the chromomagnetic QCD vacuum above the deconfinement temperature

We investigate the residual chromomagnetic nonperturbative interaction between colour sources which survives above the deconfinement temperature. This interaction is demonstrated to be attractive enough to support bound states of quarks (and gluons). Although, for heavy quarks, such bound states appear to be very shallow and thus to dissociate easily, for light quarks (and gluons), the interaction is found to be strong enough to lead to quark (gluon) pair creation in the vacuum and thus to a complete rebuild of the vacuum state. The text was submitted by the authors in English.