Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d=4d = 4

The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension $d = 4$. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case $d = 3$, at $d = 4$ additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into $d = 3$. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in $y$ (the exponent, connected with random force) and $\epsilon=4-d$. All calculations are performed in the leading one-loop approximation.Comment: 11pages, 6 figures, LATEX2e. arXiv admin note: substantial text overlap with arXiv:1611.00327; text overlap with arXiv:1611.0130

Topological and confining properties of Abelian-projected SU(3)-QCD

In this talk, we discuss several topics related to the Abelian-projected SU(3)-QCD. First of them is the Aharonov-Bohm effect emerging during the extension of this theory by the introduction of the $\Theta$-term. Another topic is devoted to various consequences of screening of the dual vector bosons by electric vortex loops. In particular, it is demonstrated that this effect modifies significantly the interaction of quarks. Next, the influence of screening to electric and magnetic field correlators in the four-dimensional Abelian-projected SU(3)-QCD is studied. Finally, the bilocal correlator of electric field strengths in the three-dimensional gas of SU(3) Abelian-projected monopoles is discussed.Comment: 6 pages, LaTeX2e, no figures, presented at High Energy Physics International Euroconference on Quantum Chromo Dynamics - QCD '00, Montpellier, France, 6-13 Jul 2000, minor corrections, subm. to Nucl. Phys. B (Proc. Suppl.

Aharonov-Bohm Effect in the Abelian-Projected SU(3)-QCD with Θ\Theta-term

By making use of the path-integral duality transformation, string representation of the Abelian-projected SU(3)-QCD with the $\Theta$-term is derived. Besides the short-range (self-)interactions of quarks (which due to the $\Theta$-term acquire a nonvanishing magnetic charge, i.e. become dyons) and electric Abrikosov-Nielsen-Olesen strings, the resulting effective action contains also a long-range topological interaction of dyons with strings. This interaction, which has the form of the 4D Gauss linking number of the trajectory of a dyon with the world-sheet of a closed string, is shown to become nontrivial at $\Theta$ not equal to $3\pi$ times an integer. At these values of $\Theta$, closed electric Abrikosov-Nielsen-Olesen strings in the model under study can be viewed as solenoids scattering dyons, which is the 4D analogue of the Aharonov-Bohm effect.Comment: 13 pages, LaTeX2e, no figure

Confining strings in the Abelian-projected SU(3)-gluodynamics II. 4D-case with θ\theta-term

The generalization of 4D confining string theory to the SU(3)-inspired case is derived. It describes string representation of the Wilson loop in the SU(3)-analogue of compact QED extended by the $\theta$-term. It is shown that although the obtained theory of confining strings differs from that of compact QED, their low-energy limits have the same functional form. This fact leads to the appearance of the string $\theta$-term in the low-energy limit of the SU(3)-inspired confining string theory. In particular, it is shown that in the extreme strong coupling regime, the crumpling of string world sheets could disappear owing to the string $\theta$-term at $\theta=\pi/12$. Finally, some characteristic features of the SU(N)-case are pointed out.Comment: 8 pages, LaTeX2e, no figures, to appear in Europhys. Letter

Various Properties of Compact QED and Confining Strings

The effects bringing about by the finiteness of the photon mass due to the Debye screening in the monopole gas in three-dimensional compact QED are studied. In this respect, a representation of the partition function of this theory as an integral over monopole densities is derived. Dual formulation of the Wilson loop yields a new theory of confining strings, which in the low-energy limit almost coincides with the one corresponding to the case when the photon is considered to be massless, whereas in the high-energy limit these two theories are quite different from each other. The confining string mass operator in the low-energy limit is also found, and its dependence on the volume of observation is studied.Comment: 7 pages, LaTeX, no figures, 1 reference is added, final version to appear in Phys. Lett.

Confining Strings in the Abelian-Projected SU(3)-Gluodynamics

String representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the monopole condensation. It is demonstrated that the summation over world sheets, bounded by the contour of the Wilson loop, is realized by the summation over branches of a certain effective multivalued potential of the monopole densities. Finally, by virtue of the so-constructed representation of the Wilson loop in terms of the monopole densities, this quantity is evaluated in the approximation of a dilute monopole gas, which makes confinement in the model under study manifest.Comment: 7 pages, new results are adde

A Possible Universal Treatment of the Field Strength Correlator in the Abelian-Projected SU(2)-Theory

An integral relation between two functions parametrizing the bilocal field strength correlator within the Stochastic Vacuum Model is obtained in the effective Abelian-projected SU(2)-theory. This relation is independent of the concrete properties of the ensemble of vortex loops, which are present in the theory under study. By virtue of the lattice result stating that the infrared asymptotic behaviours of these functions should have the same functional form, the obtained relation enables one to find these behaviours, as well as the infrared asymptotics of the bilocal correlator of densities of the vortex loops. Those turn out to be exponentials, decreasing at the inverse mass of the dual vector boson, times certain polynomials in the inverse integer powers of the distance. This result agrees with the general predictions and the existing lattice data better than the results of previous calculations, where these powers were found to be half-integer ones.Comment: 9 pages, LaTeX2e, no figures, new discussions of the obtained results are added, to appear in Phys. Lett.

Exploring correlations in the stochastic Yang-Mills vacuum

The correlation lengths of nonperturbative-nonconfining and confining stochastic background Yang-Mills fields are obtained by means of a direct analytic path-integral evaluation of the Green functions of the so-called one- and two-gluon gluelumps. Numerically, these lengths turn out to be in a good agreement with those known from the earlier, Hamiltonian, treatment of such Green functions. It is also demonstrated that the correlation function of nonperturbative-nonconfining fields decreases with the deviation of the path in this correlation function from the straight-line one.Comment: 14 pages, 3 figures; an Appendix is included, which addresses the path-dependence of the correlation function; version to appear in Phys. Lett.

Scaling Functions and Superscaling in Medium and Heavy Nuclei

The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron scaling functions. The latter are calculated in the cases of $^{62}$Ni, $^{82}$Kr, $^{118}$Sn, and $^{197}$Au nuclei on the basis of the corresponding proton and neutron density distributions which are obtained in deformed self-consistent mean-field Skyrme HF+BCS method. The results are in a reasonable agreement with the empirical data from the inclusive electron scattering from nuclei showing superscaling for negative values of $\psi'$, including those smaller than -1. This is an improvement over the relativistic Fermi gas (RFG) model predictions where $f(\psi')$ becomes abruptly zero for $\psi'\leq -1$. It is also an improvement over the CDFM calculations made in the past for nuclei with $Z\neq N$ assuming that the neutron density is equal to the proton one and using only the phenomenological charge density.Comment: 4 pages, 1 figure, ReVTeX, accepted for publication in Phys. Rev.