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

References (113) Cited by (220) ↓ Similar articles (20)

  1. Mishnyakov V, Morozov A et al Int. J. Mod. Phys. A 40 (07) (2025)
  2. Morozov A Encyclopedia of Mathematical Physics (2025) p. 168
  3. Li Ch, Mironov A, Orlov A Yu Physics Letters B 860 139170 (2025)
  4. Yang D 66 (3) (2025)
  5. Mishnyakov V, Morozov A, Reva M Physics Letters B 864 139417 (2025)
  6. Mishnyakov V, Morozov A, Reva M Nuclear Physics B 1010 116746 (2025)
  7. Mironov A, Oreshina A, Popolitov A Eur. Phys. J. C 84 (7) (2024)
  8. Mironov A, Mishnyakov V, Morozov A Nuclear Physics B 1001 116504 (2024)
  9. Mironov A, Morozov A, Popolitov A Phys. Rev. D 110 (12) (2024)
  10. Galakhov D, Morozov A, Tselousov N Phys. Rev. D 109 (6) (2024)
  11. Drachov Ya, Mironov A, Popolitov A Physics Letters B 849 138426 (2024)
  12. Kubo N, Nosaka T J. High Energ. Phys. 2024 (7) (2024)
  13. Mironov A, Morozov A et al Phys. Rev. D 110 (4) (2024)
  14. Morozov A, Oreshina A Physics Letters B 857 139006 (2024)
  15. Eynard B, Garcia-Failde E et al Ann. Henri Poincaré (2024)
  16. Morozov A Eur. Phys. J. C 83 (3) (2023)
  17. Mironov A, Morozov A J. High Energ. Phys. 2023 (3) (2023)
  18. Na W, Yang B et al Adv. Appl. Clifford Algebras 33 (1) (2023)
  19. Liu F, Mironov A et al Nuclear Physics B 993 116283 (2023)
  20. Vleeshouwers W L, Gritsev V J. Phys. A: Math. Theor. 56 185002 (2023)
  21. Mironov A, Mishnyakov V et al Eur. Phys. J. C 83 (5) (2023)
  22. Barseghyan S, Popolitov A Annals Of Physics 449 169207 (2023)
  23. Drachov Ya, Zhabin A Eur. Phys. J. C 83 (5) (2023)
  24. Mishnyakov V, Morozov A, Suprun P Nuclear Physics B 992 116245 (2023)
  25. Wang N Reports On Mathematical Physics 91 79 (2023)
  26. Morozov A, Tselousov N J. High Energ. Phys. 2023 (11) (2023)
  27. Wang G J. High Energ. Phys. 2023 (3) (2023)
  28. Mironov A, Morozov A, Popolitov A Physics Letters B 828 137038 (2022)
  29. Mishnyakov V, Suprun P Jetp Lett. 115 477 (2022)
  30. Balthazar B, Giveon A et al J. High Energ. Phys. 2022 (1) (2022)
  31. Wang N, Wu K Nuclear Physics B 974 115642 (2022)
  32. Khlaif O, Kimura T J. High Energ. Phys. 2022 (4) (2022)
  33. Wang N, Wu K 63 (2) (2022)
  34. Mishnyakov V, Oreshina A Eur. Phys. J. C 82 (6) (2022)
  35. Wang N 63 (12) (2022)
  36. Mironov A, Morozov A Physics Letters B 835 137573 (2022)
  37. Wang R, Zhang Ch-H et al Nuclear Physics B 985 115989 (2022)
  38. Mironov A, Morozov A Phys. Rev. D 106 (12) (2022)
  39. Mironov A, Mishnyakov V et al Nuclear Physics B 985 116022 (2022)
  40. Mironov A, Morozov A, Zakirova Z Physics Letters B 831 137178 (2022)
  41. Mironov A, Mishnyakov V et al Physics Letters B 829 137041 (2022)
  42. Mironov A, Morozov A, Popolitov A Physics Letters B 824 136833 (2022)
  43. Lanina E, Morozov A Eur. Phys. J. C 82 (11) (2022)
  44. Cui Zh, Bai Ya et al Nuclear Physics B 984 115986 (2022)
  45. Mironov A, Mishnyakov V, Morozov A Physics Letters B 823 136721 (2021)
  46. Morozov A J. High Energ. Phys. 2021 (10) (2021)
  47. Okuyama K, Sakai K J. High Energ. Phys. 2021 (9) (2021)
  48. Mironov A D, Morozov A Physics Letters B 819 136474 (2021)
  49. Mironov A D, Morozov A et al Lett Math Phys 111 (5) (2021)
  50. Tian K, Li S et al Physics Letters B 822 136643 (2021)
  51. Mironov A, Morozov A Physics Letters B 816 136196 (2021)
  52. Anokhina A S Phys. Part. Nuclei 52 374 (2021)
  53. Mironov A, Morozov A Eur. Phys. J. C 81 (3) (2021)
  54. Mironov A, Morozov A Physics Letters B 816 136221 (2021)
  55. Mironov A, Morozov A J. High Energ. Phys. 2021 (2) (2021)
  56. Mironov A, Mishnyakov V et al Eur. Phys. J. C 81 (12) (2021)
  57. Beccaria M, Hasan A J. High Energ. Phys. 2021 (4) (2021)
  58. Beccaria M, Tseytlin A A J. High Energ. Phys. 2021 (1) (2021)
  59. Mironov A, Mishnyakov V et al Jetp Lett. 113 728 (2021)
  60. Araujo T Nuclear Physics B 972 115566 (2021)
  61. Mironov A, Morozov A Physics Letters B 816 136268 (2021)
  62. Altland A, Sonner Ju SciPost Phys. 11 (2) (2021)
  63. Orlov A Yu Geometric Methods in Physics XXXVIII Trends In Mathematics Chapter 15 (2020) p. 221
  64. Cassia L, Lodin R, Zabzine M J. High Energ. Phys. 2020 (10) (2020)
  65. Morozov A, Tselousov N Eur. Phys. J. C 80 (12) (2020)
  66. Lodin R, Popolitov A et al Lett Math Phys 110 179 (2020)
  67. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 811 135932 (2020)
  68. Anokhina A S Phys. Part. Nuclei 51 172 (2020)
  69. Dubrovin B, Liu S-Q et al Commun. Math. Phys. 379 461 (2020)
  70. Nieri F, Pan Y, Zabzine M Commun. Math. Phys. 366 397 (2019)
  71. Mironov A, Morozov A, Zakirova Z J. High Energ. Phys. 2019 (10) (2019)
  72. Li Ch-X, Qin Zh-Yu, Shen Sh-F J. Phys. Soc. Jpn. 88 124003 (2019)
  73. Itoyama H, Mironov A, Morozov A Physics Letters B 788 76 (2019)
  74. Cassia L, Lodin R et al J. High Energ. Phys. 2019 (12) (2019)
  75. Morozov A Physics Letters B 792 205 (2019)
  76. Morozov A Eur. Phys. J. C 79 (1) (2019)
  77. van de Leur J W, Orlov A Yu J. Phys. A: Math. Theor. 51 025208 (2018)
  78. Betzios P, Gürsoy U, Papadoulaki O Nuclear Physics B 928 356 (2018)
  79. Morozov A Physics Letters B 785 175 (2018)
  80. Ivanitskii G R Phys.-Usp. 61 871 (2018)
  81. Mironov A, Morozov A Physics Letters B 785 207 (2018)
  82. Mironov A, Morozov A J. High Energ. Phys. 2018 (8) (2018)
  83. Nieri F, Pan Y et al EPJ Web Conf. 191 06005 (2018)
  84. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  85. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 784 342 (2018)
  86. Itoyama H, Mironov A, Morozov A Physics Letters B 771 180 (2017)
  87. Mironov A, Morozov A Physics Letters B 771 503 (2017)
  88. Itoyama H, Mironov A, Morozov A J. High Energ. Phys. 2017 (6) (2017)
  89. Ivanitskii G R Uspekhi Fizicheskikh Nauk 187 757 (2017)
  90. [Ivanitskii G R Phys.-Usp. 60 705 (2017)]
  91. Nedelin A, Nieri F, Zabzine M Commun. Math. Phys. 353 1059 (2017)
  92. Mironov A, Morozov A Physics Letters B 774 210 (2017)
  93. Nedelin A, Zabzine M J. High Energ. Phys. 2017 (3) (2017)
  94. Melnikov D, Mironov A, Morozov A J. High Energ. Phys. 2016 (5) (2016)
  95. Mironov A, Morozov A, Zenkevich Y Physics Letters B 762 196 (2016)
  96. Ding X-M, Li Yu, Meng L J. High Energ. Phys. 2016 (1) (2016)
  97. Procházka Tomáš J. High Energ. Phys. 2016 (10) (2016)
  98. Popolitov A Jetp Lett. 103 137 (2016)
  99. Natanzon S M, Zabrodin A V J. Phys. A: Math. Theor. 49 145206 (2016)
  100. Lafortune S, Li Ch-X J. Phys. A: Math. Theor. 49 475202 (2016)
  101. Awata H, Kanno H et al J. High Energ. Phys. 2016 (7) (2016)
  102. Morozov A, Zenkevich Y J. High Energ. Phys. 2016 (2) (2016)
  103. Morozov A A Phys. Part. Nuclei 47 775 (2016)
  104. Kanning N, Ko Yu, Staudacher M Nuclear Physics B 894 407 (2015)
  105. Alexandrov A J. High Energ. Phys. 2015 (3) (2015)
  106. Itoyama H, Yoshioka R Prog. Theor. Exp. Phys. 2015 11B103 (2015)
  107. Morozov A, Morozov A, Popolitov A Physics Letters B 749 309 (2015)
  108. Kanzieper E Constr Approx 41 615 (2015)
  109. Mironov A, Morozov A et al Int. J. Mod. Phys. A 30 1550169 (2015)
  110. Alexandrov A, Leurent S et al Nuclear Physics B 883 173 (2014)
  111. Alexandrov A Lett Math Phys 104 75 (2014)
  112. Orlov A Yu Physics Letters A 378 319 (2014)
  113. Kimura T Progress Of Theoretical And Experimental Physics 2014 103B04 (2014)
  114. Alexandrov A, Mironov A et al Jetp Lett. 100 271 (2014)
  115. Kimura T Progress Of Theoretical And Experimental Physics 2014 123A01 (2014)
  116. Alexandrov A, Mironov A et al J. High Energ. Phys. 2014 (11) (2014)
  117. Mironov A, Morozov A, Sleptsov A Eur. Phys. J. C 73 (7) (2013)
  118. Alexandrov A, Zabrodin A Journal Of Geometry And Physics 67 37 (2013)
  119. Li M, Li Ch et al 54 (4) (2013)
  120. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 27 1230001 (2012)
  121. Morozov A Yu, Morozov A Yu Teoreticheskaya Matematicheskaya Fizika 173 104 (2012)
  122. Itoyama H, Mironov A et al J. High Energ. Phys. 2012 (7) (2012)
  123. Alexandrov A J. Phys.: Conf. Ser. 343 012009 (2012)
  124. Galakhov D V, Galakhov D V i dr Teor. Mat. Fiz. 172 73 (2012)
  125. Mironov A, Morozov A, Zakirova Z Physics Letters B 711 332 (2012)
  126. Mironov A, Morozov A, Natanzon S Journal Of Geometry And Physics 62 148 (2012)
  127. Alexandrov A, Mironov A et al J. Phys. A: Math. Theor. 45 045209 (2012)
  128. Takasaki K, Takebe T Anal.Math.Phys. 2 171 (2012)
  129. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (3) (2011)
  130. Brown T W Phys. Rev. D 83 (8) (2011)
  131. Tian KeLei, He JingSong et al Sci. China Math. 54 257 (2011)
  132. Morozov A, Shakirov Sh Journal Of Geometry And Physics 61 708 (2011)
  133. ALEXANDROV A Mod. Phys. Lett. A 26 2193 (2011)
  134. Mironov A, Morozov A, Morozov A Nuclear Physics B 843 534 (2011)
  135. Shakirov Sh Physics Letters A 375 984 (2011)
  136. Mironov A D, Mironov A D i dr Teor. Mat. Fiz. 166 3 (2011) [Mironov A D, Morozov A Yu, Natanzon S M Theor Math Phys 166 1 (2011)]
  137. Alexandrov A Nuclear Physics B 851 620 (2011)
  138. Tian K, Hea J et al Chin. Ann. Math. Ser. B 32 895 (2011)
  139. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (2) (2011)
  140. Osipov V A, Kanzieper E Annals Of Physics 325 2251 (2010)
  141. Mironov A, Morozov A J. Phys. A: Math. Theor. 43 195401 (2010)
  142. Mironov A, Morozov A J. High Energ. Phys. 2010 (4) (2010)
  143. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 25 3173 (2010)
  144. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 162 3 (2010) [Morozov A Yu Theor Math Phys 162 1 (2010)]
  145. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2010 (2) (2010)
  146. Mironov A, Mironov S et al J. Phys. A: Math. Theor. 43 055402 (2010)
  147. MOROZOV A, SHAKIROV SH Mod. Phys. Lett. A 24 2659 (2009)
  148. Galakhov D, Itoyama H et al Nuclear Physics B 823 289 (2009)
  149. Osipov V A, Kanzieper E J. Phys. A: Math. Theor. 42 475101 (2009)
  150. Wang D 50 (7) (2009)
  151. Morozov A, Shakirov Sh J. High Energy Phys. 2009 002 (2009)
  152. Morozov A, Shakirov Sh J. High Energy Phys. 2009 003 (2009)
  153. Morozov A, Shakirov Sh J. High Energy Phys. 2009 064 (2009)
  154. Mironov A, Morozov A Physics Letters B 680 188 (2009)
  155. ALEXANDROV A, MIRONOV A et al Int. J. Mod. Phys. A 24 4939 (2009)
  156. Dimakis A, Müller-Hoissen F Generalized Lie Theory in Mathematics, Physics and Beyond Chapter 2 (2009) p. 9
  157. Alexandrov A, Mironov A, Morozov A J. High Energy Phys. 2009 053 (2009)
  158. Mironov A, Morozov A J. High Energy Phys. 2009 024 (2009)
  159. Akhmedov E T Phys. Atom. Nuclei 72 1574 (2009)
  160. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 157 208 (2008) [Morozov A Yu Theor Math Phys 157 1542 (2008)]
  161. DOLOTIN V, MOROZOV A Int. J. Mod. Phys. A 23 3613 (2008)
  162. Morozov A J. High Energy Phys. 2008 086 (2008)
  163. Kostov I K, Petkova V B Nuclear Physics B 769 175 (2007)
  164. Okuyama K Physics Letters B 645 275 (2007)
  165. Alexandrov A, Mironov A, Morozov A Physica D: Nonlinear Phenomena 235 126 (2007)
  166. Aleksandrov A S, Alexandrov A S i dr Teor. Mat. Fiz. 150 179 (2007) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 150 153 (2007)]
  167. Chekhov L O, Chekhov L O i dr Usp. Mat. Nauk 61 93 (2006)
  168. Zabrodin A NATO Science Series II: Mathematics, Physics And Chemistry Vol. Applications of Random Matrices in PhysicsMATRIX MODELS AND GROWTH PROCESSES: FROM VISCOUS FLOWS TO THE QUANTUM HALL EFFECT221 Chapter 8 (2006) p. 261
  169. Chekhov L J. Phys. A: Math. Gen. 39 8857 (2006)
  170. ALEXANDROV A, MIRONOV A, MOROZOV A Int. J. Mod. Phys. A 21 2481 (2006)
  171. Ellwood I, Hashimoto A J. High Energy Phys. 2006 002 (2006)
  172. Aleksandrov A S, Alexandrov A S i dr Teor. Mat. Fiz. 142 419 (2005) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 142 349 (2005)]
  173. Klemm A Fortschritte Der Physik 53 720 (2005)
  174. Okuyama K J. High Energy Phys. 2005 002 (2005)
  175. Morozov A NATO Science Series II: Mathematics, Physics And Chemistry Vol. String Theory: From Gauge Interactions to CosmologyChallenges of Matrix Models208 Chapter 6 (2005) p. 129
  176. Orlov A Yu Acta Appl Math 86 131 (2005)
  177. Sedrakyan T A Nuclear Physics B 729 526 (2005)
  178. Chiantese S, Klemm A, Runkel I J. High Energy Phys. 2004 033 (2004)
  179. YU ORLOV A Int. J. Mod. Phys. A 19 276 (2004)
  180. ALEXANDROV A, MOROZOV A, MIRONOV A Int. J. Mod. Phys. A 19 4127 (2004)
  181. Maldacena Ju, Moore G et al J. High Energy Phys. 2004 020 (2004)
  182. Konopelchenko B G, Moro A J. Phys. A: Math. Gen. 37 L105 (2004)
  183. JURČO BRANISLAV Mod. Phys. Lett. A 19 1661 (2004)
  184. Mironov A D, Mironov A D i dr Teor. Mat. Fiz. 135 434 (2003)
  185. Morozov A, Niemi A J Nuclear Physics B 666 311 (2003)
  186. Itoyama H, Morozov A Nuclear Physics B 657 53 (2003)
  187. Konopelchenko B, Moro A J. Phys. A: Math. Gen. 36 11837 (2003)
  188. Zinn-Justin P, Zuber J-B J. Phys. A: Math. Gen. 36 3173 (2003)
  189. Dymarsky A, Pestun V Phys. Rev. D 67 (12) (2003)
  190. Fyodorov Ya V, Strahov E J. Phys. A: Math. Gen. 36 3203 (2003)
  191. Kanzieper E Phys. Rev. Lett. 89 (25) (2002)
  192. Mironov A, Morozov A Physics Letters B 524 217 (2002)
  193. Marshakov A V Uspekhi Fizicheskikh Nauk 172 977 (2002)
  194. Gorbunov I V, Sharapov A A Physics Letters B 531 255 (2002)
  195. Konopelchenko B G, Schief W K J. Phys. A: Math. Gen. 35 6125 (2002)
  196. Dijkgraaf R, Vafa C Nuclear Physics B 644 21 (2002)
  197. GERASIMOV A, MOROZOV A, SELIVANOV K Int. J. Mod. Phys. A 16 1531 (2001)
  198. Chekhov L O, Chekhov L O Teor. Mat. Fiz. 127 179 (2001)
  199. Orlov A Yu, Scherbin D M Physica D: Nonlinear Phenomena 152-153 51 (2001)
  200. Paniak L D, Szabo R J Nuclear Physics B 593 671 (2001)
  201. NISSIMOV E, PACHEVA S Int. J. Mod. Phys. A 16 2311 (2001)
  202. Braden H W, Mironov A, Morozov A Physics Letters B 514 293 (2001)
  203. Gorskii A S, Gorsky A S Teor. Mat. Fiz. 125 3 (2000)
  204. Konopelchenko B, Alonso L M Physics Letters A 258 272 (1999)
  205. Kakei S J. Phys. Soc. Jpn. 68 2875 (1999)
  206. Morozov A Particles and Fields Chapter 5 (1999) p. 127
  207. Zarembo K L, Makeenko Yu M Uspekhi Fizicheskikh Nauk 168 3 (1998)
  208. Aratyn H, Nissimov E, Pacheva S Physics Letters A 244 245 (1998)
  209. Mironov A D, Mironov A D Teor. Mat. Fiz. 114 163 (1998) [Mironov A D Theor Math Phys 114 127 (1998)]
  210. Akhmedov E T Physics Letters B 442 152 (1998)
  211. Gorsky A, Marshakov A et al Nuclear Physics B 527 690 (1998)
  212. Orlov A Yu, Winternitz P Theor Math Phys 113 1393 (1997)
  213. Itoyama H, Morozov A Nuclear Physics B 491 529 (1997)
  214. Yoltukhovskii M V Neurophysiology 29 137 (1997)
  215. Vinternits P, Winternitz P i dr Teor. Mat. Fiz. 113 231 (1997)
  216. Aratyn H, Nissimov E, Pacheva S Physics Letters A 228 164 (1997)
  217. Matone M Journal Of Geometry And Physics 21 381 (1997)
  218. Orlov A Yu, Winternitz P 38 4644 (1997)
  219. Semenoff G W, Szabo R J Theor Math Phys 104 823 (1995)
  220. Juriev D V Journal Of Geometry And Physics 16 275 (1995)
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