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

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

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

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

Residues and Topological Yang-Mills Theory in Two Dimensions

A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in some detail. The method of the diagonalization of a matrix valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.Comment: 23 pages, some references added, to appear in Rev.Math.Phy

2D Yang-Mills Theory as a Matrix String Theory

Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If these sectors are taken into account the partition function is different from the standard one found in the literature and the invariance of the theory under modular transformations of the torus appears to hold in a stronger sense. The twisted sectors are in one-to-one correspondence with the coverings of the torus without branch points, so they define by themselves a string theory. A possible duality between this string theory and the Gross-Taylor string is discussed, and the problems that one encounters in generalizing this approach to interacting strings are pointed out. This talk is based on a previous paper by the same authors, but it contains some new results and a better interpretation of the results already obtained.Comment: 11 pages, LaTeX, 2 figures included with epsf. Talk presented at the 2nd Conference on Quantum aspects of Gauge Theories, Supersymmetry and Unification, Corfu, Greece, 21-26 September 199

Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces

The path integral computation of field strength correlation functions for two dimensional Yang-Mills theories over Riemann surfaces is studied. The calculation is carried out by abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.Comment: final version to appear in Int. Jour. Mod. Phys. A, minor corrections, added a few comments on Wilson loops and non-abelian Stokes theore