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B. Rusakov

Publications and source records attributed to B. Rusakov.

7 recordsLinked to original sources
arXiv1997

Exactly Soluble QCD and Confinement of Quarks

An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory.

hep-th↗
arXiv1997

Two-dimensional dynamics of QCD_3

Exact loop-variables formulation of pure gauge lattice QCD_3 is derived from the Wilson version of the model. The observation is made that the resulting model is two-dimensional. This significant feature is shown to be a unique property of the gauge field. The model is defined on the infinite genus surface which covers regularly the original three-dimensional lattice. Similar transformation applied to the principal chiral field model in two and three dimensions for comparison with QCD.

hep-th↗
arXiv1994

Lattice QCD as a theory of interacting surfaces

Pure gauge lattice QCD at arbitrary D is considered. Exact integration over link variables in an arbitrary D-volume leads naturally to an appearance of a set of surfaces filling the volume and gives an exact expression for functional of their boundaries. The interaction between each two surfaces is proportional to their common area and is realized by a non-local matrix differential operator acting on their boundaries. The surface self-interaction is given by the QCD$_2$ functional of boundary. Partition functions and observables (Wilson loop averages) are written as an averages over all configurations of an integer-valued field living on a surfaces.

hep-th↗
arXiv1994

Large N Phase Transitions and Multi-Critical Behaviour in Generalized 2D QCD

Using matrix model techniques we investigate the large N limit of generalized 2D Yang-Mills theory. The model has a very rich phase structure. It exhibits multi-critical behavior and reveals a third order phase transitions at all genera besides {\it torus}. This is to be contrasted with ordinary 2D Yang-Mills which, at large N, exhibits phase transition only for spherical topology.

hep-th↗
arXiv1993

Large-N quantum gauge theories in two dimensions

The partition function of a two-dimensional quantum gauge theory in the large-$N$ limit is expressed as the functional integral over some scalar field. The large-$N$ saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus $g>0$. The existence of a non-trivial saddle point is closely related to the weak coupling behavior of the theory. Possible applications of the method to higher dimensions are briefly discussed.

hep-th↗
arXiv1992

From hermitian matrix model to lattice gauge theory

I consider a lattice model of a gauge field interacting with matrix-valued scalars in $D$ dimensions. The model includes an adjustable parameter $\s$, which plays role of the string tension. In the limit $\s=\infty$ the model coincides with Kazakov-Migdal's ``induced QCD", where Wilson loops obey a zero area law. The limit $\s=0$, where Wilson loops $W(C)=1$ independently of the size of the loop, corresponds to the Hermitian matrix model. For $D=2$ and $D=3$ I show that the model obeys the same combinatorics as the standard LGT and therefore one may expect the area law behavior. In the strong coupling expansion such a behavior is demonstrated.

hep-th↗