Supersymmetric Matrix Models and the Meander Problem

1996/01/25 by Yuri Makeenko, Makeenko, Yuri, Iouri Chepelev +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Random Matrices and Applications #Stochastic processes and statistical mechanics #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9601139

31 pages, Latex; v2: the name of one of the authors changed -- Iouri Chepelev former Hla Win Pe

openalex publication_date 1996/01/25 · arxiv created 1997/09/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider matrix-model representations of the meander problem which describes, in particular, combinatorics for foldings of closed polymer chains. We introduce a supersymmetric matrix model for describing the principal meander numbers. This model is of the type proposed by Marinari and Parisi for discretizing a superstring in D=1 while the supersymmetry is realized in D=0 as a rotational symmetry between bosonic and fermionic matrices. Using non-commutative sources, we reformulate the meander problem in a Boltzmannian Fock space whose annihilation and creation operators obey the Cuntz algebra. We discuss also the relation between the matrix models describing the meander problem and the Kazakov-Migdal model on a D-dimensional lattice.

Cited by

• Meanders: a direct enumeration approach
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

Related

• Applications of Supersymmetric Matrix Models
• Matrix Model Combinatorics: Applications to Folding and Coloring
• A Diagrammatic Approach to the Meander Problem
• Generating series and matrix models for meandric systems with one shallow side
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders