Matrix models among integrable theories: Forced hierarchies and operator formalism

S. Kharchev, A. Marshakov, A. Mironov, A. Orlov, A. Zabrodin

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)


We consider a variety of matrix models as a certain subspace of the whole space of integrable theories, namely, the subspace of forced ("semi-infinite") hierarchies. The integrability is discussed in terms of orthogonality conditions which generalize those of matrix models. The explicit solutions of matrix models are proposed using the fermionic representation of τ-functions. Various generalizations of matrix models associated with the generic point of the infinite flag space are introduced. The simplest example of a hermitian matrix model is investigated in detail and the first non-trivial example of unitary matrix model is also discussed. Finally, we point out that the cancellation of the partition function by positive Virasoro generators is a common thing for general τ-functions in integrable models and discuss the special role of the Virasoro algebra in matrix models, which can be interpreted as a gauge-fixing condition in the corresponding "string field theory".

Original languageEnglish
Pages (from-to)569-601
Number of pages33
JournalNuclear Physics B
Issue number3
Publication statusPublished - 9 Dec 1991
Externally publishedYes


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