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

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 Solution of the Cauchy Problem for the Loop Equation in Turbulence

Under certain conditions, imposed on the viscosity of the fluid, initial data and the class of contours under consideration, the Cauchy problem with finite values of time for the loop equation in turbulence with Gaussian random forces is solved by making use of the smearing procedure for the loop space functional Laplacian. The solution obtained depends on the initial data and its functional derivatives and on the potential of the random forces.Comment: 6 pages, LaTeX, no figure

Dynamics of the Universal Confining String Theory on the Loop Space

Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one. In the functional momentum representation the obtained equation decouples into two independent ones, which describe the dynamics of the transverse and longitudinal components of the area derivative of the Wilson loop. At some critical value of the momentum discontinuity, which can be determined from a certain equation, the transverse component does not propagate. Next, we derive the equation for the momentum Wilson loop, where on the left-hand side stands the sum of the squares of the momentum discontinuities, multiplied by the loop, which describes its free propagation, while the right-hand side describes the interaction of the loop with the functional vorticity tensor current. Finally, using the method of inversion of the functional Laplacian, we obtain for the Wilson loop in the coordinate representation a simple Volterra type-II linear integral equation, which can be treated perturbatively.Comment: 7 pages, LaTeX, no figures, a remark is adde

Gluodynamics String as a Low-Energy Limit of the Universal Confining String Theory

An effective string theory emerging from the bilocal approximation to the Method of Vacuum Correlators in gluodynamics is shown to be well described by the 4D theory of the massive Abelian Kalb-Ramond field interacting with the string, which is known to be the low-energy limit of the Universal Confining String Theory. The mass of the Kalb-Ramond field in this approach plays the role of the inverse correlation length of the vacuum, and it is shown that in the massless limit string picture disappears. The background field method, known in the theory of nonlinear sigma models, is applied to derivation of the effective action, quadratic in quantum fluctuations around a given (e.g. minimal) string world-sheet.Comment: 11 pages, LaTeX, no figures, 2 references are updated, to be published in Phys. Lett.

Stochastic loop equations

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and the equation for the Quenched Master Field Wilson loop is derived. The regularized version of one of the obtained equations is presented and applied to derivation of the equation for the bilocal field correlator. The momentum loop dynamics is also investigated.Comment: 13 page