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)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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

References (113) Cited by (213) Similar articles (20) ↓

V.G. Knizhnik “Multiloop amplitudes in the theory of quantum strings and complex geometry” Sov. Phys. Usp. 32 945–971 (1989)
A.Yu. Morozov “Anomalies in gauge theories” Sov. Phys. Usp. 29 993–1039 (1986)
A.P. Protogenov “Anyon superconductivity in strongly-correlated spin systems” Sov. Phys. Usp. 35 (7) 535–571 (1992)
A.I. Vainshtein, V.I. Zakharov et al “ABC of instantons” Sov. Phys. Usp. 25 195–215 (1982)
K.L. Zarembo, Yu.M. Makeenko “An introduction to matrix superstring models” Phys. Usp. 41 1–23 (1998)
M.I. Rabinovich, M.K. Muezzinoglu “Nonlinear dynamics of the brain: emotion and cognition” Phys. Usp. 53 357–372 (2010)
G.R. Ivanitskii, A.B. Medvinskii, M.A. Tsyganov “From the dynamics of population autowaves generated by living cells to neuroinformatics” Phys. Usp. 37 961–989 (1994)
V.A. Rubakov “Large and infinite extra dimensions” Phys. Usp. 44 871–893 (2001)
M.A. Tsyganov, V.N. Biktashev et al “Waves in systems with cross-diffusion as a new class of nonlinear waves” Phys. Usp. 50 263–286 (2007)
V.V. Klinshov, V.I. Nekorkin “Synchronization of delay-coupled oscillator networks” Phys. Usp. 56 1217–1229 (2013)
D.S. Chernavskii “The origin of life and thinking from the viewpoint of modern physics” Phys. Usp. 43 151–176 (2000)
V.V. Smolyaninov “Spatio-temporal problems of locomotion control” Phys. Usp. 43 991–1053 (2000)
V.I. Arnol’d “Singularities, bifurcations, and catastrophes” Sov. Phys. Usp. 26 1025–1037 (1983)
G.R. Ivanitskii “21st century: what is life from the perspective of physics?” Phys. Usp. 53 327–356 (2010)
G.N. Borisyuk, R.M. Borisyuk et al “Models of neural dynamics in brain information processing — the developments of ’the decade’” Phys. Usp. 45 1073–1095 (2002)
M.I. Vysotskii, R.B. Nevzorov “Selected problems of supersymmetry phenomenology” Phys. Usp. 44 919–930 (2001)
V.A. Rubakov, P.G. Tinyakov “Infrared-modified gravities and massive gravitons” Phys. Usp. 51 759–792 (2008)
G.B. Lesovik, I.A. Sadovskyy “Scattering matrix approach to the description of quantum electron transport” Phys. Usp. 54 1007–1059 (2011)
V.I. Ogievetskii, L. Mezincescu “Boson-fermion symmetries and superfields” Sov. Phys. Usp. 18 960–982 (1975)
L.N. Lipatov “Integrability properties of high energy dynamics in the multi-color QCD” Phys. Usp. 47 325–339 (2004)

The list is formed automatically.