3,617 research outputs found
Large-N quantum gauge theories in two dimensions
The partition function of a two-dimensional quantum gauge theory in the
large- limit is expressed as the functional integral over some scalar field.
The large- 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 . 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
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
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