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

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