Strings, Matrix Models, and Meanders

Abstract

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.

12 pages, 4 Latex figures, uses espcrc2.sty Talk at the 29th Ahrenshoop Symp., Buckow, Germany, Aug.29 - Sep.2, 1995

References in corpus (11)

• Induced QCD at Large N
• The Multicritical Kontsevich-Penner Model
• Multi-spin systems on a randomly triangulated surface
• Some Remarks About Induced QCD
• Adjoint Fermion Matrix Models
• Some Remarks About the Two-Matrix Penner Model and the Kazakov-Migdal Model
• Large-N Reduction, Master Field and Loop Equations in Kazakov-Migdal Model
• Correlators of the Kazakov-Migdal Model
• Critical Scaling and Continuum Limits in the D>1 Kazakov-Migdal Model
• Evaluation of Observables in the Gaussian $N=\infty$ Kazakov-Migdal Model
• Critical scaling in the matrix model on the Bethe tree

Cited by in corpus (5)

• Meanders: Exact Asymptotics
• A transfer matrix approach to the enumeration of plane meanders
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Exact Meander Asymptotics: a Numerical Check
• Supermatrix models, loop equations, and duality