On the origin of integrability in matrix models
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.
scientific article; zbMATH DE number 4210710