Integrability and matrix models

A.Yu. Morozov
Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ’conformal’ (multicomponent) and Kontsevich models are considered in some detail, together with the Ward identites (’W-constraints’), determinantal formulas and continuum limits, taking one kind of model into another. Subtle points and directions of the future research are also discussed.

PACS: 02.10.+b, 11.17.+y
DOI: 10.1070/PU1994v037n01ABEH000001
URL: https://ufn.ru/en/articles/1994/1/a/
Web of Science

A1994NA86300001
Citation: Morozov A Yu "Integrability and matrix models" Phys. Usp. 37 1–55 (1994)

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%0 Journal Article
%T Integrability and matrix models
%A A. Yu. Morozov
%I Physics-Uspekhi
%D 1994
%J Phys. Usp.
%V 37
%N 1
%P 1-55
%U https://ufn.ru/en/articles/1994/1/a/
%U https://doi.org/10.1070/PU1994v037n01ABEH000001

Оригинал: Морозов А Ю «Интегрируемость и матричные модели» УФН 164 3–62 (1994); DOI: 10.3367/UFNr.0164.199401a.0003