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The generalization of the effective action [1] of the quark-antiquark system in the confining vacuum is performed for the case of arbitrary quark masses. The interaction of quarks is described by the averaged Wilson loop for which we use the minimal area law asymptotics.The system is quantized by the path integral method and the quantum Hamiltonian is obtained. It contains not only quark degrees of freedom but also the string energy density.As well as in the equal masses case [1] two dynamical regimes are found [2]: for large orbital excitations (l ≫ 1) the system is represented as rotating string, which leads to asymptotically linear Regge trajectories, while at small l one obtains a potential-like relativistic or nonrelativistic regime.In the limiting cases of light-light and heavy-light mesons a unified description is developed [2]. For the Regge trajectories one obtains nearly straight-line patterns with the slope very close to 1/2πσ and 1/πσ correspondingly. The upper bound on the light quark(s) masses which doesn't change considerably this property of the trajectories is also found. I n t r o d u c t i o nRecently the new approach to study nonperturbative large distance dynamics of quarkantiquark system in the confining vacuum has been developed and the Hamiltonian for the case of equal quark masses has been obtained [1]. In the present paper we consider the general case of arbitrary quark masses. The effective Hamiltonian of the system is derived (for a short report see [2]) and properties of its spectrum are analysed.With the help of vacuum correlator formalizm [3] we represent gauge invariant Green function of the qq system in a form where all dynamics of the interaction is described by the averaged Wilson loop operator. Starting from the QCD Lagrangian and making use of the minimal area 1

We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise general formula and demonstrate its anomalous behavior at large parameter of noncommutativity for the simplest nonplanar diagram of genus 1. We discuss various UV/IR regularizations of the two-dimensional noncommutative gauge theory in the axial gauge and, using the noncommutative loop equation, construct a consistent regularization.

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Employing the nonabelian duality transformation [25], I derive the Gauge String form of certain D ≥ 3 lattice Yang-Mills ( Y M D ) theories in the strong coupling (SC) phase. With the judicious choice of the actions, in D ≥ 3 our construction generalizes the Gross-Taylor stringy reformulation of the continuous Y M 2 on a 2d manifold. Using the Eguchi-Kawai model as an example, we develope the algorithm to determine the weights w[M ] for connected YM-flux worldsheets M immersed into the 2d skeleton of a D ≥ 3 base-lattice. Owing to the invariance of w[M ] under a continuous group of area-preserving worldsheet homeomorphisms, the set of the weights {w[M ]} can be used to define the theory of the smooth YM-fluxes which unambiguously refers to a particular continuous Y M D system. I argue that the latter Y M D models (with a finite ultraviolet cut-off) for sufficiently large bare coupling constant(s) are reproduced, to all orders in 1/N , by the smooth Gauge String thus associated. The asserted Y M D /String duality allows to make a concrete prediction for the 'bare' string tension σ 0 which implies that (in the large N SC regime) the continuous Y M D systems exhibit confinement for D ≥ 2 . The resulting pattern is qualitatively consistent (in the extreme D = 4 SC limit) with the Witten's proposal motivated by the AdS/CFT correspondence.