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.Comment: TAUP-2204-94, 12pp., LaTe

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.Comment: CERN-TH.7390/94 and TAUP-2191-94, 6pp, LaTe

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.Comment: 6pp., Latex, TAUP-2012-92 (revised: few changes, some references added

Wilson Loops in Large N QCD on a Sphere

Wilson loop averages of pure gauge QCD at large N on a sphere are calculated by means of Makeenko-Migdal loop equation.Comment: Phys.Lett.B329 (1994) 338 (minor corrections in accordance to published version, several Latex figures are removed and available upon request

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.Comment: 12 pages, LaTeX (substantial revision and reorganization of the text; the emphasis redirected to the physics of the approach; no change in the resulting model and conclusion

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.Comment: 6 pages, LaTeX (revision: references added

Morphological plasticity of astroglia: Understanding synaptic microenvironment

Memory formation in the brain is thought to rely on the remodeling of synaptic connections which eventually results in neural network rewiring. This remodeling is likely to involve ultrathin astroglial protrusions which often occur in the immediate vicinity of excitatory synapses. The phenomenology, cellular mechanisms, and causal relationships of such astroglial restructuring remain, however, poorly understood. This is in large part because monitoring and probing of the underpinning molecular machinery on the scale of nanoscopic astroglial compartments remains a challenge. Here we briefly summarize the current knowledge regarding the cellular organisation of astroglia in the synaptic microenvironment and discuss molecular mechanisms potentially involved in use-dependent astroglial morphogenesis. We also discuss recent observations concerning morphological astroglial plasticity, the respective monitoring methods, and some of the newly emerging techniques that might help with conceptual advances in the area. GLIA 2015