497 research outputs found
Strings, Matrix Models, and Meanders
I briefly review the present status of bosonic strings and discretized random
surfaces in D>1 which seem to be in a polymer rather than stringy phase. As an
explicit example of what happens, I consider the Kazakov-Migdal model with a
logarithmic potential which is exactly solvable for any D (at large D for an
arbitrary potential). I discuss also the meander problem and report some new
results on its representation via matrix models and the relation to the
Kazakov-Migdal model. A supersymmetric matrix model is especially useful for
describing the principal meanders.Comment: 12 pages, 4 Latex figures, uses espcrc2.sty Talk at the 29th
Ahrenshoop Symp., Buckow, Germany, Aug.29 - Sep.2, 199
Large-N Reduction, Master Field and Loop Equations in Kazakov-Migdal Model
I study the large-N reduction a la Eguchi--Kawai in the Kazakov--Migdal
lattice gauge model. I show that both quenching and twisting prescriptions lead
to the coordinate-independent master field. I discuss properties of loop
averages in reduced as well as unreduced models and demonstrate those coincide
in the large mass expansion. I derive loop equations for the Kazakov--Migdal
model at large N and show they are reduced for the quadratic potential to a
closed set of two equations. I find an exact strong coupling solution of these
equations for any D and extend the result to a more general interacting
potential.Comment: 17 pages (1 Latex figure), ITEP-YM-6-92 The figure is replaced by
printable on
The First Thirty Years of Large-N Gauge Theory
I review some developments in the large-N gauge theory since 1974. The main
attention is payed to: multicolor QCD, matrix models, loop equations, reduced
models, 2D quantum gravity, free random variables, noncommutative theories,
AdS/CFT correspondence.Comment: 13.1pp., Latex, 2 figs; v2: 2 refs added. Talk at Large Nc QCD 200
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