Generation of matrix models by Ŵ-operators

2009/02/21 by А. Морозов, A. Morozov, Sh. Shakirov · 6 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #hep-th

paper · pdf · doi:10.1088/1126-6708/2009/04/064

published as JHEP 0904:064,2009 · 30 pages

arxiv created 2009/02/21 · openalex publication_date 2009/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in external field and the Hurwitz-Kontsevitch model, for which we suggest an elegant matrix-model representation. In all these examples, the relevant W-operators belong to the W₃-algebra.

Citations

• Large Random Matrices: Eigenvalue Distribution
• U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Gaussian matrix model in an external field and non-intersecting Brownian motions
• Random Matrix Theories in Quantum Physics: Common Concepts
• A Perturbative Window into Non-Perturbative Physics
• Normal random matrix ensemble as a growth problem
• A nonperturbative treatment of two-dimensional quantum gravity
• Gauge symmetry and supersymmetry of multiple M2-branes
• Gluing of Surfaces with Polygonal Boundaries
• Resultants and Contour Integrals

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• Enumerative Geometry, Tau-Functions and Heisenberg–Virasoro Algebra