On the origin of integrability in matrix models
type: Item
instance of: scholarly article
title: On the origin of integrability in matrix models
zbMATH Open document ID: 0732.35100
DOI: 10.1007/BF02102036
author: Emil J. Martinec
published in: Communications in Mathematical Physics
publication date: 1991-01-01T00:00:00Z
review text: One-matrix model \(Z=\int {\mathcal D}\Phi e^{-V(\Phi)}\), \(V(\Phi)=\sum t_ ktr\{\Phi^ k\}\) (unitary one-matrix model, two-matrix model) of string theory is related to Toda hierarchy (quaternionic Toda hierarchy, 2-d Toda hierarchy) by using the orthogonal polynomial transcription of the matrix problem. Appropriately defined \(\tau\)-function (different from the standard free fermion setting) of the Toda lattice is realized by a matrix model partition function.
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 83C27
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 4210710
zbMATH Keywords: string theory
zbMATH Keywords: Toda hierarchy
zbMATH Keywords: orthogonal polynomial transcription
zbMATH Keywords: Toda lattice
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4210710