RSS feeds
ÐóññêèéEnglish
Issue 7, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1994

 / 

January

←  →

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.

Fulltext pdf (1.5 MB)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ìîðîçîâ À Þ «Èíòåãðèðóåìîñòü è ìàòðè÷íûå ìîäåëè» ÓÔÍ 164 3–62 (1994); DOI: 10.3367/UFNr.0164.199401a.0003

References (113) Cited by (208) ↓ Similar articles (20)

  1. Mironov A, Mishnyakov V, Morozov A Nuclear Physics B 1001 116504 (2024)
  2. Kubo N, Nosaka T J. High Energ. Phys. 2024 (7) (2024)
  3. Galakhov D, Morozov A, Tselousov N Phys. Rev. D 109 (6) (2024)
  4. Eynard B, Garcia-Failde E et al Ann. Henri Poincaré (2024)
  5. Drachov Ya, Mironov A, Popolitov A Physics Letters B 849 138426 (2024)
  6. Vleeshouwers W L, Gritsev V J. Phys. A: Math. Theor. 56 185002 (2023)
  7. Na W, Yang B et al Adv. Appl. Clifford Algebras 33 (1) (2023)
  8. Wang G J. High Energ. Phys. 2023 (3) (2023)
  9. Wang N Reports On Mathematical Physics 91 79 (2023)
  10. Morozov A, Tselousov N J. High Energ. Phys. 2023 (11) (2023)
  11. Liu F, Mironov A et al Nuclear Physics B 993 116283 (2023)
  12. Barseghyan S, Popolitov A Annals Of Physics 449 169207 (2023)
  13. Mishnyakov V, Morozov A, Suprun P Nuclear Physics B 992 116245 (2023)
  14. Mironov A, Mishnyakov V et al Eur. Phys. J. C 83 (5) (2023)
  15. Drachov Ya, Zhabin A Eur. Phys. J. C 83 (5) (2023)
  16. Morozov A Eur. Phys. J. C 83 (3) (2023)
  17. Mironov A, Morozov A J. High Energ. Phys. 2023 (3) (2023)
  18. Wang R, Zhang Ch-H et al Nuclear Physics B 985 115989 (2022)
  19. Wang N, Wu K 63 (2) (2022)
  20. Mironov A, Morozov A Physics Letters B 835 137573 (2022)
  21. Cui Zh, Bai Ya et al Nuclear Physics B 984 115986 (2022)
  22. Mishnyakov V, Suprun P Jetp Lett. 115 477 (2022)
  23. Balthazar B, Giveon A et al J. High Energ. Phys. 2022 (1) (2022)
  24. Khlaif O, Kimura T J. High Energ. Phys. 2022 (4) (2022)
  25. Mironov A, Morozov A, Popolitov A Physics Letters B 828 137038 (2022)
  26. Wang N 63 (12) (2022)
  27. Mironov A, Mishnyakov V et al Physics Letters B 829 137041 (2022)
  28. Lanina E, Morozov A Eur. Phys. J. C 82 (11) (2022)
  29. Wang N, Wu K Nuclear Physics B 974 115642 (2022)
  30. Mishnyakov V, Oreshina A Eur. Phys. J. C 82 (6) (2022)
  31. Mironov A, Morozov A, Popolitov A Physics Letters B 824 136833 (2022)
  32. Mironov A, Mishnyakov V et al Nuclear Physics B 985 116022 (2022)
  33. Mironov A, Morozov A, Zakirova Z Physics Letters B 831 137178 (2022)
  34. Mironov A, Morozov A Phys. Rev. D 106 (12) (2022)
  35. Beccaria M, Hasan A J. High Energ. Phys. 2021 (4) (2021)
  36. Altland A, Sonner Ju SciPost Phys. 11 (2) (2021)
  37. Morozov A J. High Energ. Phys. 2021 (10) (2021)
  38. Beccaria M, Tseytlin A A J. High Energ. Phys. 2021 (1) (2021)
  39. Araujo T Nuclear Physics B 972 115566 (2021)
  40. Mironov A, Morozov A Physics Letters B 816 136268 (2021)
  41. Mironov A D, Morozov A Physics Letters B 819 136474 (2021)
  42. Mironov A, Morozov A Eur. Phys. J. C 81 (3) (2021)
  43. Anokhina A S Phys. Part. Nuclei 52 374 (2021)
  44. Mironov A, Mishnyakov V et al Eur. Phys. J. C 81 (12) (2021)
  45. Mironov A, Mishnyakov V, Morozov A Physics Letters B 823 136721 (2021)
  46. Tian K, Li S et al Physics Letters B 822 136643 (2021)
  47. Mironov A, Morozov A Physics Letters B 816 136221 (2021)
  48. Mironov A D, Morozov A et al Lett Math Phys 111 (5) (2021)
  49. Mironov A, Mishnyakov V et al Jetp Lett. 113 728 (2021)
  50. Mironov A, Morozov A Physics Letters B 816 136196 (2021)
  51. Okuyama K, Sakai K J. High Energ. Phys. 2021 (9) (2021)
  52. Mironov A, Morozov A J. High Energ. Phys. 2021 (2) (2021)
  53. Cassia L, Lodin R, Zabzine M J. High Energ. Phys. 2020 (10) (2020)
  54. Lodin R, Popolitov A et al Lett Math Phys 110 179 (2020)
  55. Orlov A Yu Geometric Methods in Physics XXXVIII Trends In Mathematics Chapter 15 (2020) p. 221
  56. Dubrovin B, Liu S-Q et al Commun. Math. Phys. 379 461 (2020)
  57. Morozov A, Tselousov N Eur. Phys. J. C 80 (12) (2020)
  58. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 811 135932 (2020)
  59. Anokhina A S Phys. Part. Nuclei 51 172 (2020)
  60. Morozov A Eur. Phys. J. C 79 (1) (2019)
  61. Morozov A Physics Letters B 792 205 (2019)
  62. Cassia L, Lodin R et al J. High Energ. Phys. 2019 (12) (2019)
  63. Mironov A, Morozov A, Zakirova Z J. High Energ. Phys. 2019 (10) (2019)
  64. Li Ch-X, Qin Zh-Yu, Shen Sh-F J. Phys. Soc. Jpn. 88 124003 (2019)
  65. Itoyama H, Mironov A, Morozov A Physics Letters B 788 76 (2019)
  66. Nieri F, Pan Y, Zabzine M Commun. Math. Phys. 366 397 (2019)
  67. Nieri F, Pan Y et al EPJ Web Conf. 191 06005 (2018)
  68. Mironov A, Morozov A J. High Energ. Phys. 2018 (8) (2018)
  69. Morozov A Physics Letters B 785 175 (2018)
  70. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  71. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 784 342 (2018)
  72. Betzios P, Gürsoy U, Papadoulaki O Nuclear Physics B 928 356 (2018)
  73. Mironov A, Morozov A Physics Letters B 785 207 (2018)
  74. van de Leur J W, Orlov A Yu J. Phys. A: Math. Theor. 51 025208 (2018)
  75. Mironov A, Morozov A Physics Letters B 774 210 (2017)
  76. Nedelin A, Nieri F, Zabzine M Commun. Math. Phys. 353 1059 (2017)
  77. Mironov A, Morozov A Physics Letters B 771 503 (2017)
  78. Ivanitskii G R Uspekhi Fizicheskikh Nauk 187 757 (2017)
  79. Itoyama H, Mironov A, Morozov A J. High Energ. Phys. 2017 (6) (2017)
  80. Itoyama H, Mironov A, Morozov A Physics Letters B 771 180 (2017)
  81. Nedelin A, Zabzine M J. High Energ. Phys. 2017 (3) (2017)
  82. Awata H, Kanno H et al J. High Energ. Phys. 2016 (7) (2016)
  83. Morozov A A Phys. Part. Nuclei 47 775 (2016)
  84. Morozov A, Zenkevich Y J. High Energ. Phys. 2016 (2) (2016)
  85. Popolitov A Jetp Lett. 103 137 (2016)
  86. Lafortune S, Li Ch-X J. Phys. A: Math. Theor. 49 475202 (2016)
  87. Melnikov D, Mironov A, Morozov A J. High Energ. Phys. 2016 (5) (2016)
  88. Procházka Tomáš J. High Energ. Phys. 2016 (10) (2016)
  89. Mironov A, Morozov A, Zenkevich Y Physics Letters B 762 196 (2016)
  90. Ding X-M, Li Yu, Meng L J. High Energ. Phys. 2016 (1) (2016)
  91. Natanzon S M, Zabrodin A V J. Phys. A: Math. Theor. 49 145206 (2016)
  92. Alexandrov A J. High Energ. Phys. 2015 (3) (2015)
  93. Mironov A, Morozov A et al Int. J. Mod. Phys. A 30 1550169 (2015)
  94. Itoyama H, Yoshioka R Prog. Theor. Exp. Phys. 2015 11B103 (2015)
  95. Kanning N, Ko Yu, Staudacher M Nuclear Physics B 894 407 (2015)
  96. Morozov A, Morozov A, Popolitov A Physics Letters B 749 309 (2015)
  97. Kanzieper E Constr Approx 41 615 (2015)
  98. Kimura T Progress Of Theoretical And Experimental Physics 2014 103B04 (2014)
  99. Kimura T Progress Of Theoretical And Experimental Physics 2014 123A01 (2014)
  100. Alexandrov A, Mironov A et al Jetp Lett. 100 271 (2014)
  101. Alexandrov A Lett Math Phys 104 75 (2014)
  102. Alexandrov A, Leurent S et al Nuclear Physics B 883 173 (2014)
  103. Orlov A Yu Physics Letters A 378 319 (2014)
  104. Alexandrov A, Mironov A et al J. High Energ. Phys. 2014 (11) (2014)
  105. Mironov A, Morozov A, Sleptsov A Eur. Phys. J. C 73 (7) (2013)
  106. Alexandrov A, Zabrodin A Journal Of Geometry And Physics 67 37 (2013)
  107. Li M, Li Ch et al 54 (4) (2013)
  108. Mironov A, Morozov A, Zakirova Z Physics Letters B 711 332 (2012)
  109. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 27 1230001 (2012)
  110. Morozov A Yu, Morozov A Yu Teoreticheskaya Matematicheskaya Fizika 173 104 (2012)
  111. Alexandrov A J. Phys.: Conf. Ser. 343 012009 (2012)
  112. Galakhov D V, Galakhov D V i dr Teor. Mat. Fiz. 172 73 (2012)
  113. Alexandrov A, Mironov A et al J. Phys. A: Math. Theor. 45 045209 (2012)
  114. Itoyama H, Mironov A et al J. High Energ. Phys. 2012 (7) (2012)
  115. Mironov A, Morozov A, Natanzon S Journal Of Geometry And Physics 62 148 (2012)
  116. Takasaki K, Takebe T Anal.Math.Phys. 2 171 (2012)
  117. 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)]
  118. Alexandrov A Nuclear Physics B 851 620 (2011)
  119. Shakirov Sh Physics Letters A 375 984 (2011)
  120. Morozov A, Shakirov Sh Journal Of Geometry And Physics 61 708 (2011)
  121. Mironov A, Morozov A, Morozov A Nuclear Physics B 843 534 (2011)
  122. Brown T W Phys. Rev. D 83 (8) (2011)
  123. Tian KeLei, He JingSong et al Sci. China Math. 54 257 (2011)
  124. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (2) (2011)
  125. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (3) (2011)
  126. Tian K, Hea J et al Chin. Ann. Math. Ser. B 32 895 (2011)
  127. ALEXANDROV A Mod. Phys. Lett. A 26 2193 (2011)
  128. Mironov A, Morozov A J. Phys. A: Math. Theor. 43 195401 (2010)
  129. Mironov A, Mironov S et al J. Phys. A: Math. Theor. 43 055402 (2010)
  130. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 162 3 (2010) [Morozov A Yu Theor Math Phys 162 1 (2010)]
  131. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2010 (2) (2010)
  132. Osipov V A, Kanzieper E Annals Of Physics 325 2251 (2010)
  133. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 25 3173 (2010)
  134. Mironov A, Morozov A J. High Energ. Phys. 2010 (4) (2010)
  135. Mironov A, Morozov A J. High Energy Phys. 2009 024 (2009)
  136. ALEXANDROV A, MIRONOV A et al Int. J. Mod. Phys. A 24 4939 (2009)
  137. Morozov A, Shakirov Sh J. High Energy Phys. 2009 064 (2009)
  138. Dimakis A, Müller-Hoissen F Generalized Lie Theory in Mathematics, Physics and Beyond Chapter 2 (2009) p. 9
  139. Wang D 50 (7) (2009)
  140. Morozov A, Shakirov Sh J. High Energy Phys. 2009 002 (2009)
  141. MOROZOV A, SHAKIROV SH Mod. Phys. Lett. A 24 2659 (2009)
  142. Mironov A, Morozov A Physics Letters B 680 188 (2009)
  143. Morozov A, Shakirov Sh J. High Energy Phys. 2009 003 (2009)
  144. Akhmedov E T Phys. Atom. Nuclei 72 1574 (2009)
  145. Alexandrov A, Mironov A, Morozov A J. High Energy Phys. 2009 053 (2009)
  146. Osipov V A, Kanzieper E J. Phys. A: Math. Theor. 42 475101 (2009)
  147. Galakhov D, Itoyama H et al Nuclear Physics B 823 289 (2009)
  148. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 157 208 (2008) [Morozov A Yu Theor Math Phys 157 1542 (2008)]
  149. DOLOTIN V, MOROZOV A Int. J. Mod. Phys. A 23 3613 (2008)
  150. Morozov A J. High Energy Phys. 2008 086 (2008)
  151. 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)]
  152. Kostov I K, Petkova V B Nuclear Physics B 769 175 (2007)
  153. Okuyama K Physics Letters B 645 275 (2007)
  154. Alexandrov A, Mironov A, Morozov A Physica D: Nonlinear Phenomena 235 126 (2007)
  155. Chekhov L O, Chekhov L O i dr Usp. Mat. Nauk 61 93 (2006)
  156. 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
  157. Ellwood I, Hashimoto A J. High Energy Phys. 2006 002 (2006)
  158. ALEXANDROV A, MIRONOV A, MOROZOV A Int. J. Mod. Phys. A 21 2481 (2006)
  159. Chekhov L J. Phys. A: Math. Gen. 39 8857 (2006)
  160. Sedrakyan T A Nuclear Physics B 729 526 (2005)
  161. 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
  162. 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)]
  163. Klemm A Fortschritte Der Physik 53 720 (2005)
  164. Orlov A Yu Acta Appl Math 86 131 (2005)
  165. Okuyama K J. High Energy Phys. 2005 002 (2005)
  166. JURČO BRANISLAV Mod. Phys. Lett. A 19 1661 (2004)
  167. Chiantese S, Klemm A, Runkel I J. High Energy Phys. 2004 033 (2004)
  168. Maldacena Ju, Moore G et al J. High Energy Phys. 2004 020 (2004)
  169. YU ORLOV A Int. J. Mod. Phys. A 19 276 (2004)
  170. ALEXANDROV A, MOROZOV A, MIRONOV A Int. J. Mod. Phys. A 19 4127 (2004)
  171. Konopelchenko B G, Moro A J. Phys. A: Math. Gen. 37 L105 (2004)
  172. Dymarsky A, Pestun V Phys. Rev. D 67 (12) (2003)
  173. Mironov A D, Mironov A D i dr Teor. Mat. Fiz. 135 434 (2003)
  174. Konopelchenko B, Moro A J. Phys. A: Math. Gen. 36 11837 (2003)
  175. Fyodorov Ya V, Strahov E J. Phys. A: Math. Gen. 36 3203 (2003)
  176. Itoyama H, Morozov A Nuclear Physics B 657 53 (2003)
  177. Morozov A, Niemi A J Nuclear Physics B 666 311 (2003)
  178. Zinn-Justin P, Zuber J-B J. Phys. A: Math. Gen. 36 3173 (2003)
  179. Dijkgraaf R, Vafa C Nuclear Physics B 644 21 (2002)
  180. Mironov A, Morozov A Physics Letters B 524 217 (2002)
  181. Gorbunov I V, Sharapov A A Physics Letters B 531 255 (2002)
  182. Kanzieper E Phys. Rev. Lett. 89 (25) (2002)
  183. Konopelchenko B G, Schief W K J. Phys. A: Math. Gen. 35 6125 (2002)
  184. Marshakov A V Uspekhi Fizicheskikh Nauk 172 977 (2002)
  185. Chekhov L O, Chekhov L O Teor. Mat. Fiz. 127 179 (2001)
  186. Braden H W, Mironov A, Morozov A Physics Letters B 514 293 (2001)
  187. GERASIMOV A, MOROZOV A, SELIVANOV K Int. J. Mod. Phys. A 16 1531 (2001)
  188. NISSIMOV E, PACHEVA S Int. J. Mod. Phys. A 16 2311 (2001)
  189. Orlov A Yu, Scherbin D M Physica D: Nonlinear Phenomena 152-153 51 (2001)
  190. Paniak L D, Szabo R J Nuclear Physics B 593 671 (2001)
  191. Gorskii A S, Gorsky A S Teor. Mat. Fiz. 125 3 (2000)
  192. Kakei S J. Phys. Soc. Jpn. 68 2875 (1999)
  193. Morozov A Particles and Fields Chapter 5 (1999) p. 127
  194. Konopelchenko B, Alonso L M Physics Letters A 258 272 (1999)
  195. Akhmedov E T Physics Letters B 442 152 (1998)
  196. Gorsky A, Marshakov A et al Nuclear Physics B 527 690 (1998)
  197. Mironov A D, Mironov A D Teor. Mat. Fiz. 114 163 (1998) [Mironov A D Theor Math Phys 114 127 (1998)]
  198. Aratyn H, Nissimov E, Pacheva S Physics Letters A 244 245 (1998)
  199. Zarembo K L, Makeenko Yu M Uspekhi Fizicheskikh Nauk 168 3 (1998)
  200. Orlov A Yu, Winternitz P Theor Math Phys 113 1393 (1997)
  201. Yoltukhovskii M V Neurophysiology 29 137 (1997)
  202. Vinternits P, Winternitz P i dr Teor. Mat. Fiz. 113 231 (1997)
  203. Itoyama H, Morozov A Nuclear Physics B 491 529 (1997)
  204. Orlov A Yu, Winternitz P 38 4644 (1997)
  205. Aratyn H, Nissimov E, Pacheva S Physics Letters A 228 164 (1997)
  206. Matone M Journal Of Geometry And Physics 21 381 (1997)
  207. Juriev D V Journal Of Geometry And Physics 16 275 (1995)
  208. Semenoff G W, Szabo R J Theor Math Phys 104 823 (1995)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions