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Reviews of topical problems


Integrability and matrix models


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.

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Fulltext is also available at DOI: 10.1070/PU1994v037n01ABEH000001
PACS: 02.10.+b, 11.17.+y
DOI: 10.1070/PU1994v037n01ABEH000001
URL: https://ufn.ru/en/articles/1994/1/a/
A1994NA86300001
Citation: Morozov A Yu "Integrability and matrix models" Phys. Usp. 37 1–55 (1994)
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Îðèãèíàë: Ìîðîçîâ À Þ «Èíòåãðèðóåìîñòü è ìàòðè÷íûå ìîäåëè» ÓÔÍ 164 3–62 (1994); DOI: 10.3367/UFNr.0164.199401a.0003

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