String Nature of Confinement in (Non-)Abelian Gauge Theories

Recent progress achieved in the solution of the problem of confinement in various (non-)Abelian gauge theories by virtue of a derivation of their string representation is reviewed. The theories under study include QCD within the so-called Method of Field Correlators, QCD-inspired Abelian-projected theories, and compact QED in three and four space-time dimensions. Various nonperturbative properties of the vacua of the above mentioned theories are discussed. The relevance of the Method of Field Correlators to the study of confinement in Abelian models, allowing for an analytical description of this phenomenon, is illustrated by an evaluation of field correlators in these models.Comment: 100 pages, LaTeX2e, no figures, 1 table, based on the Ph.D. thesises at the Humboldt University of Berlin (1999) (available under http://dochost.rz.hu-berlin.de) and the Institute of Theoretical and Experimental Physics, Moscow (2000), new results are included, extended with respect to the journal versio

Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models

Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. The second one is the strongly non-equilibrium reaction-diffusion system, known as Gribov process and equivalent to the Reggeon field theory. The turbulent mixing is modelled by the Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum k^{-d-\xi}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent \xi and the spatial dimension d, the both systems exhibit four different types of critical behaviour, associated with four possible fixed points of the renormalization group equations. The most interesting point corresponds to a new type of critical behaviour, in which the nonlinearity and turbulent mixing are both relevant, and the critical exponents depend on d, \xi and the degree of compressibility. For the both models, compressibility enhances the role of the nonlinear terms in the dynamical equations: the region in the d-\xi plane, where the new nontrivial regime is stable, is getting much wider as the degree of compressibility increases. In its turn, turbulent transfer becomes more efficient due to combined effects of the mixing and the nonlinear terms.Comment: 25 pages, 4 figure

On the Topological Term in the String Representation of the Wilson Loop in the Dilute Instanton Gas

A topological term related to the number of self-intersections of the string world-sheet is shown to emerge in the string representation of the Wilson loop in the dilute instanton gas. The coupling constant of this term occurs to be proportional to the topological charge of the instanton gas under consideration.Comment: 4 pages, LaTeX, no figure

Worldline Casting of the Stochastic Vacuum Model and Non-Perturbative Properties of QCD: General Formalism and Applications

The Stochastic Vacuum Model for QCD, proposed by Dosch and Simonov, is fused with a Worldline casting of the underlying theory, i.e. QCD. Important, non-perturbative features of the model are studied. In particular, contributions associated with the spin-field interaction are calculated and both the validity of the loop equations and of the Bianchi identity are explicitly demonstrated. As an application, a simulated meson-meson scattering problem is studied in the Regge kinematical regime. The process is modeled in terms of the "helicoidal" Wilson contour along the lines introduced by Janik and Peschanski in a related study based on a AdS/CFT-type approach. Working strictly in the framework of the Stochastic Vacuum Model and in a semiclassical approximation scheme the Regge behavior for the Scattering amplitude is demonstrated. Going beyond this approximation, the contribution resulting from boundary fluctuation of the Wilson loop contour is also estimated.Comment: 37 pages, 1 figure. Final version to appear in Phys.Rev.

Anomalous exponents in the rapid-change model of the passive scalar advection in the order ϵ3\epsilon^{3}

Field theoretic renormalization group is applied to the Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $- <{\bf v}(t,{\bf x}){\bf v}(t',{\bf x'})> \propto\delta(t-t')|{\bf x}-{\bf x'} |^{\epsilon}$. Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order $\epsilon^{3}$ of the $\epsilon$ expansion. The nature and the convergence of the $\epsilon$ expansion in the models of turbulence is are briefly discussed.Comment: 4 pages; REVTeX source with 3 postscript figure

REDUCING THE MAGNETIC VISCOSITY EFFECT ON TEM SOUNDING DATA

Siberian Traps magnetic viscosity affects and makes it difficult to interpret TEM sounding data obtained during oil and gas exploration in the south of the Siberian platform. In this paper, we present and discuss a method for decreasing magnetic viscosity effect on TEM data. The method is based on estimating magnetic viscosity contribution to the total transient response using TEM data measured with multi-offset arrays

Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ε3\varepsilon^{3}

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function \propto\delta(t-t')/k^{d+\eps}. Inertial-range anomalous exponents, identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients, are calculated within the $\varepsilon$ expansion to order $\varepsilon^{3}$ (three-loop approximation), including the exponents in anisotropic sectors. The main goal of the paper is to give the complete derivation of this third-order result, and to present and explain in detail the corresponding calculational techniques. The character and convergence properties of the $\varepsilon$ expansion are discussed; the improved ``inverse'' $\varepsilon$ expansion is proposed and the comparison with the existing nonperturbative results is given.Comment: 34 pages, 5 figures, REVTe