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Обзоры актуальных проблем


Интегрируемость и матричные модели


Государственный научный центр Российской Федерации «Институт теоретической и экспериментальной физики им. А.И. Алиханова», ул. Б. Черемушкинская 25, Москва, 117259, Российская Федерация

Обзор теории матричных моделей с точки зрения ее связи с интегрируемыми иерархиями. Приведен весьма подробный анализ дискретных одноматричных, двухматричных «конформных» (многокомпонентных) моделей и модели Концевича, а также тождеств Уорда (’W-условий’), детерминантных формул и непрерывных пределов, переводящих один вид моделей в другой. Обсуждаются вопросы, требующие дополнительной разработки, а также направления дальнейших исследований.

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English fulltext is available at DOI: 10.1070/PU1994v037n01ABEH000001
PACS: 02.10.+b, 11.17.+y
DOI: 10.3367/UFNr.0164.199401a.0003
URL: https://ufn.ru/ru/articles/1994/1/a/
A1994NA86300001
Цитата: Морозов А Ю "Интегрируемость и матричные модели" УФН 164 3–62 (1994)
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English citation: Morozov A Yu “Integrability and matrix models” Phys. Usp. 37 1–55 (1994); DOI: 10.1070/PU1994v037n01ABEH000001

Список литературы (113) ↓ Статьи, ссылающиеся на эту (215) Похожие статьи (20)

  1. Морозов А УФН 162 (8) 84 (1992); Morozov A Sov. Phys. Usp. 35 671 (1992)
  2. Klebanov I, Polyakov A Mod. Phys. Lett. A 6 3273 (1991)
  3. Witten E Nucl. Phys. B 373 187 (1992)
  4. Marshakov A, Mironov A, Olshanetsky M et al. "c=rG Theories of W G-Gravity: the Set of Observables as a Model of Simply-Laced G" Preprint ITEP-M2/92 hep-th/9203043, to appear in Nucl. Phys. B
  5. Alekseev A, Shatashvili S Nucl. Phys. B 329 719 (1989)
  6. Gerasimov A, Lebedev D et al. Int. J. Mod. Phys. A 6 977 (1991); Morozov A Mod. Phys. Lett. A 6 1525 (1992)
  7. Its A, Izergin A, Korepin V, Slavnov N et al. HEPTH (1992), December
  8. Witten E Comm. Math. Phys. 117 353 (1988); Witten E Comm. Math. Phys. 118 411 (1988)
  9. Witten E Nucl. Phys. B 340 281 (1990); Witten E Surv. Diff. Geom. 1 243 (1991)
  10. Dijkgraaf R, Witten E Nucl. Phys. B 342 486 (1990)
  11. Birmingham D, Blau M, Rakowski M, Thompson G Phys. Rep. 209 129 (1991)
  12. Belavin A, Polyakov A, Zamolodchikov A Nucl. Phys. B 241 333 (1984)
  13. Книжник В УФН 159 (3) 401 (1989); Knizhnik V Sov. Phys. Usp. 32 945 (1989)
  14. Переломов А и др. Комплексная геометрия и теория струн (М.: ВИНИТИ, 1990); English translation, Perelomov A et al. Complex Geometry and String Theory (Berlin: Springer, 1991)
  15. Фейгин Б, Фукс Д Функц. анализ и его прилож. 16 (2) 247 (1982); Фейгин Б, Фукс Д Функц. анализ и его прилож. 17 (3) 91 (1983); Dotsenko V, Fateev V Nucl. Phys B 240 312 (1984); Dotsenko V, Fateev V Feigin B, Frenkel E Commun. Math. Phys. 128 161 (1990)
  16. Gerasimov A, Marshakov A, Olshanetsky M, Shatashvili S et al. Int. J. Mod. Phys. A 5 2495 (1990)
  17. Losev A "Descendants Constructed from Matter Fields and K Saito Higher Residue Pairing in Topological L-G Theories Coupled to Topological Gravity" Preprint TPI-MINN (1992), May; Losev A, Polyubin I "On Connection between Topological Landau-Ginzburg Gravity and Integrable Systems" preprint ITEP/UU-ITP (1992), December
  18. Migdal A Phys. Rep. 102 199 (1983)
  19. Kazakov V Mod. Phys. Lett. A 4 2125 (1989)
  20. Brezin E, Kazakov V Phys. Lett. B 236 144 (1990); Douglas M, Shenker S Nucl. Phys. B 335 635 (1990); Gross D, Migdal A Phys. Rev. Lett. 64 127 (1990)
  21. Shabat G, Voevodski V Sov. Math. Dokl. 39 38 (1989); Levin A, et al. Phys. Lett. B 243 207 (1990); Smit D-J Commun. Math. Phys. 143 253 (1992)
  22. Концевич М Функц. анализ и его прилож. 25 (2) 50 (1991)
  23. Witten E Proc. of the NYC Conf., June (1991)
  24. Marshakov A, Mironov A et al. Phys. Lett. B 274 280 (1992)
  25. Kazakov V, Migdal A "Induced QCD at Large N" Preprint PUPT-1322 (1992)
  26. Gerasimov A, Marshakov A, Mironov A, Orlov A, et al. Nucl. Phys. B 357 565 (1991)
  27. Mironov A, et al. Phys. Lett. B 252 47 (1990); Ambjorn J, Jurkiewicz J, Makeenko Yu Phys. Lett. B 251 517 (1990); Itoyama H, Matsuo Y Phys. Lett. B 255 202 (1991)
  28. Makeenko Yu, Marshakov A, Mironov A, et al. Nucl. Phys. B 356 574 (1991)
  29. Fukuma M, Kawai H, Nakayama R Int. J. Mod. Phys. A 6 1385 (1991); Dijkgraaf R, Verlinde E, Verlinde H Nucl. Phys. B 348 565 (1991)
  30. Kharchev S, Marshakov A, Mironov A, Zabrodin A, et al. Phys. Lett. B 275 311 (1992); Kharchev S, Marshakov A, Mironov A, Zabrodin A, et al. Nucl. Phys. B 380 181 (1992)
  31. Dijkgraaf R "Intersection Theory, Integrable Hierarchies and Topological Field Theory" Preprint IASSNS-HEP-91/91; Dijkgraaf R "Intersection Theory, Integrable Hierarchies and Topological Field Theory" hep-th/9201003
  32. Kontsevich M Commun. Math. Phys. 147 (1) 1 (1992)
  33. Adler M, Moerbeke P van Comm. Math. Phys. 147 25 (1992); Adler M, Moerbeke P van Itzykson C, Zuber J-B "Combinatorics of the Modular Group II. The Kontsevich Integrals" Preprint SPhT/92-001, to appear in Int. J. Mod. Phys. A
  34. Crnkovich C, Ginsparg P, Moore G Phys. Lett. B 237 196 (1990); Gross D, Migdal A Phys. Rev. Lett. 64 717 (1990); Brezin E, Douglas M, Kazakov V, Shenker S Phys. Lett. B 237 43 (1990)
  35. Chekhov L, Makeenko Yu Phys. Lett. B 278 271 (1992)
  36. Kharchev S, Marshakov A, Mironov A et al. "Generalized Kontsevich Model versus To da Hierarchy and Discrete Matrix Models" Preprint ITEP-M3/92; Kharchev S, Marshakov A, Mironov A et al. "Generalized Kontsevich Model versus To da Hierarchy and Discrete Matrix Models" hep-th/9203043, to appear in Nucl. Phys. B
  37. Douglas M Phys. Lett. B 238 176 (1990)
  38. Marshakov A, Mironov A et al. Mod. Phys. Lett. A 7 1345 (1992)
  39. Marshakov A, Mironov A et al. Phys. Lett. B 265 99 (1991); Mironov A, Pakuliak S "Double-Scaling Limit in the Matrix Models of a New Type" Preprint FIAN/TD/05-92; Kharchev S, Marshakov A, Mironov A, Pakuliak S et al. "Conformal Matrix Models as an Alternative to Conventional Multi-matrix Models" preprint ITEP-M4/92; Kharchev S, Marshakov A, Mironov A, Pakuliak S et al. "Conformal Matrix Models as an Alternative to Conventional Multi-matrix Models" hep-th/9208044, to appear in Nuc l. Phys. B
  40. Kharchev S, Marshakov A, Mironov A et al. "Landau-Ginzburg Topological Theories in the Framework of GRM and Equivalent Hierarchies" Preprint ITEP-M5/92; Kharchev S, Marshakov A, Mironov A et al. "Landau-Ginzburg Topological Theories in the Framework of GRM and Equivalent Hierarchies" hep-th/9208046, to appear in Mod. Phys. Lett.
  41. Kharchev S, Marshakov A "Topological versus Non-Topological Theories" preprint FIAN/TD-15/92
  42. Date E, Jimbo M, Kashiwara M, Miwa T "Transformation Groups for Soliton Equations" RIMS-394 (1982), February
  43. Witten E "Two-Dimensional Gauge Theories Revisited" Preprint IASSNS-HEP 92/15
  44. Niemi A, Tirkkonen O "On Exact Evaluation of Path Integrals" Preprint UU-ITP 3/93
  45. Gerasimov A, Makeenko Yu, Marshakov A, Mironov A, Orlov A et al. Mod. Phys. Lett. A 6 3079 (1991)
  46. Brezin E, Itzykson C, Parisi G, Zuber J-B Commun. Math. Phys. 59 35 (1978)
  47. Frenkel I, Kac V Inv. Math. 62 23 (1980); Segal G Commun. Math. Phys. 80 301 (1981)
  48. Bershadsky M, Ooguri H Commun. Math. Phys. 126 49 (1989)
  49. Bershadsky M Commun. Math. Phys. 1397 1 (1991)
  50. Bais F A, Tjin T, Driel P van Nucl. Phys. B 357 632 (1991)
  51. Feher L, O'Raifeartaigh L, Ruelle O, Tsutsui I, Wipf A "On the General Structure of H amiltonian Reductions of WZW Theory" Preprint DIAS-STP-91 UdeM-LPN-TH-71/91
  52. Замолодчиков А ТМФ 63 1205 (1985); Lukianov S, Fateev V Int. J. Mod. Phys. A 3 507 (1988)
  53. Alvarez-Gaume L et al. Preprint CERN (1991)
  54. Gross D, Newman M Phys. Lett. B 266 291 (1991)
  55. Mikhailov A Preprint ITEP-UU (1993), March
  56. Chekhov L, Makeenko Yu Phys. Lett. B 278 271 (1992)
  57. Gava E, Narain K Phys. Lett. B 263 213 (1991)
  58. Shifman M, Turbiner A et al. Int. J. Mod. Phys. A 5 2953 (1990)
  59. Migdal A "Exact Solution of Induced Lattice Gauge Theory at Large N" Preprint PUPT-1323 (1992), June
  60. Itzykson C, Zuber J-B J. Math. Phys. 21 411 (1980)
  61. Harish-Chandra Am. J. Math. 79 87 (1957)
  62. Семенов-Тян-Шанский М Изв. АН СССР. Сер. физ. 40 562 (1976)
  63. Alekseev A, Faddeev L, Shatashvili S J. Geom. Phys. 3 (1989)
  64. Duistermaat J, Heckman G Invent. Math. 69 259 (1982)
  65. Blau M, Keski-Vakkuri E, Niemi A Phys. Lett. B 246 92 (1990); Keski-Vakkuri E, Niemi A, Semenoff G, Tirkkonen O Phys. Rev. D 44 3899 (1991); Hietamaki A, Niemi A, Palo K et al. Phys. Lett. B 263 417 (1991); Niemi A, Palo K et al. Phys. Lett. B 271 365 (1991); Niemi A, Palo K et al. Nucl. Phys. B 377 295 (1992)
  66. Kogan I, Semenoff G, Weiss N et al. "Area Law and Continuum Limit in "Induced QCD"" Preprint UBCTP92-26/ITEPM6/92; Kogan I, Semenoff G, Weiss N et al. "Area Law and Continuum Limit in "Induced QCD"" hep-th/9208012, to appear in Nucl. Phys. B
  67. Morozov A "Pair Correlator in the Itzykson-Zuber Integral" Preprint ITEP-M10/92 (1992); Morozov A "Pair Correlator in the Itzykson-Zuber Integral" (1992) hep-th/9209074, to appear in Mod. Phys. Lett. A September
  68. Shatashvili S "Correlation Functions in the Itzyks on-Zuber Model" Preprint IASSNS-HEP-92/61 (1992), September
  69. Vinet L et al. "q-Hypergeometric Functions in the Free Field Formalism" Preprint ITEP-M9/92 (1992), August
  70. Miwa T Proc. Jpn. Acad. 58 9 (1982); Saito S Phys. Rev. Lett. 59 1798 (1987); Saito S Phys. Rev. D 36 1819 (1987)
  71. Caselle M, D'Adda A, Panzer S "Exact Solution of D = 1 Kazakov-Migdal Induced Gauge Theory" Preprint DFTT-38/92 (1992), July
  72. Kogan I, Semenoff G, Weiss N et al. "Continuum Limits of "Induced QCD" :Lessons of the Gaussian Model at d=1 and beyond" Preprint ITEP-M7/92, UBCTP 92-27 (1992), to appear in Int. J. Mod. Phys. A August
  73. Olshanetsky M, Perelomov A Phys. Rep. 71 (5) (1981)
  74. Freund P, Zabrodin A Phys. Lett. B 284 283 (1992); Freund P, Zabrodin A Commun. Math. Phys. 147 277 (1992); Freund P, Zabrodin A Zabrodin A Mod. Phys. Lett. A 7 441 (1992)
  75. Freund P, Zabrodin A "Excitation Scattering in Integrable Models and Hall-Littlewood-Kerov Polynomials" hep-th/9208063
  76. Turbiner A Функц. анализ и его прилож. 22 33 (1988); Turbiner A Commun. Math. Phys. 118 467 (1988); Shifman M, Turbiner A Commun. Math. Phys. 120 347 (1989)
  77. Perelomov A, Rosly A, Shifman M, Turbiner A et al. Int. J. Mod. Phys. A 5 803 (1990)
  78. Halpern M, Kiritsis E Mod. Phys. Lett. A 4 1973 (1989); Halpern M, Kiritsis E, Obers N, Porrati M, Yamron J Int. J. Mod. Phys. A 5 2275 (1990)
  79. Niemi A, Pasanen P Phys. Lett. B 253 349 (1991)
  80. Polychronakos A Nucl. Phys. B 324 597 (1989); Leinaas J, Myrheim J Phys. Rev. B 37 9286 (1988); Brink L, Hansson T, Konstein S, Vasiliev M "The Calogero Model-Anyonic Representation, Fermionic Extension and Super symmetry" Preprint USITP-92-14/Goteborg ITP-92-53 (1993), January
  81. Gorsky A, Nekrasov N "Hamiltonian Systems of Calogero Type and Two-Dimensional Yang-Mills Theory" Preprint ITEP-20/93, UUITP-6/93 (1993), March
  82. Sato M RIMS Kokyuroku 439 30 (1981); Sato M, Sato Ya Lect. Notes Num. Appl. Anal. 5 259 (1982); Segal G, Wilson G Publ. I.H.E.S. 61 1 (1985)
  83. Kac V Infinite Dimensional Lie Algebras (Cambridge: Cambridge University Press, 1985)
  84. Orlov A, Shulman E Lett. Math. Phys. 12 171 (1986); Grinevich P, Orlov A "Problems of Mo dern Quantum Field Theory" Proceedings of Kiev Conference (Eds A Belavin et al.) (Berlin: Springer, 1989)
  85. de Voos K Nucl. Phys. B 375 478 (1992)
  86. Hirota R "Direct Methods in Soliton Theory" Topics in Current Physics Vol. 17 (Eds R Bullough, P Caudrey) (New York: Springer, 1980) p. 157
  87. Friedan D, Shenker S Phys. Lett. B 175 287 (1986); Ishibashi N, Matsuo Y, Ooguri H Mod. Phys. Lett. A 2 119 (1987); Alvarez-Gaume L, Gomez C, Reina C Phys. Lett. B 190 55 (1987); Witten E Commun. Math. Phys. 113 529 (1988); Morozov A Phys. Lett. B 196 325 (1987)
  88. Jimbo M, Miwa T, Sato M Holonomic Quantum Fields I-V Vol. 14 (Kyoto: RIMS, Kyoto Univ., 1978) p. 223; Jimbo M, Miwa T, Sato M Holonomic Quantum Fields I-V 15 (Kyoto: RIMS, Kyoto Univ.) 201, 577, 871, 1531 (1979)
  89. Kharchev S, Marshakov A, Mironov A, Orlov A, Zabrodin A Nucl. Phys. B 366 569 (1991)
  90. Ueno K, Takasaki K Adv. Stud. Pure Math. 4 1 (1984)
  91. Bowick M, Shewitz D et al. Nucl. Phys. B 354 496 (1991)
  92. Hirota R, Ohta Y, Satsuma J J. Phys. Soc. Jpn. 57 1901 (1988)
  93. Kac V, van de Leur J "The n-Component KP Hierarchy and Representation Theory" Preprint (1993), January
  94. Moore G Commun. Math. Phys. 133 261 (1990)
  95. Witten E "The N Matrix Model and Gauged WZW Models" Preprint IAS-HEP-91/26, to appear in to appear in Nucl. Phys. B
  96. Krichever I Commun. Math. Phys. 143 415 (1992); Dubrovin B Nucl. Phys. B 379 627 (1992)
  97. Takasaki K, Takebe K "S Diff (2) KP Hierarchy" Preprint RIMS-814 (1991), October
  98. Makeenko Yu, Semenoff G Int. J. Mod. Phys. A 6 3455 (1991); Gross D, Newman M Phys. Lett. B 266 291 (1991)
  99. Di Francesco P, Itzykson C, Zuber J-B Commun. Math. Phys. 151 193 (1993)
  100. Takebe T "From General Zakharov-Shabat Equations to the KP and the Toda-Lattice Hierarchies" Preprint RIMS-779 (1991)
  101. Date E, Jimbo M, Kashiwara M, Miwa T Transformation Groups for Soliton Equations RIMS-394 (1982), February
  102. Kharchev S et al. Preprint ITEP-M12/92
  103. Novikov S, Manakov S, Pitaevski L, Zakharov V Theory of Solitons (New York: Plenum, 1984)
  104. Fairlie D, Govaerts J et al. Nucl. Phys. B 373 214 (1992); Fairlie D, Govaerts J Phys. Lett. B 281 49 (1992); Fairlie D, Govaerts J J. Math. Phys. 33 3542 (1992)
  105. Makeenko Yu, Migdal A Phys. Lett. B 88 135 (1979)
  106. Penner R Commun. Math. Phys. 113 299 (1987); Penner R J. Differ. Geom. 27 35 (1988)
  107. Martinec E Phys. Lett. B 217 431 (1989); Martinec E "Criticalities, catastrophe and compactigications" V Knizhnik Memorial Volume (1980); Vafa C, Warner N Phys. Lett. B 218 51 (1989); Greene B, Vafa C, Warner N Nucl. Phys. B 324 371 (1989); Lerche W, Vafa C, Warner N Nucl. Phys. B 324 427 (1989); Vafa C Mod. Phys. Lett. A 6 337 (1990); Dijkgraaf R, Verlinde E, Verlinde H Nucl. Phys. B 352 59 (1991); Li K Nucl. Phys. B 354 711 (1991)
  108. Elitzur S, Forge A, Rabinovici E Nucl. Phys. B 388 131 (1992)
  109. Cecotti S, Vafa C Nucl. Phys. B 367 359 (1991)
  110. Kac V, Schwarz A Phys. Lett. B 257 329 (1991)
  111. Semenoff G, Weiss N "Symmetry and Observables in Induced QCD" Preprint UBC (1993), March; to appear in, Semenoff G, Weiss N Proc. of Rakhov School on Mathematical Physics, String Theory and Quantum Gravity, Rakhov, Ukraine, October 1992
  112. Klebanov I Proc. of 1991 Trieste Spring School on Strings and Quantum Gravity (Ed. J Harvey et al.) (Singapore: World Scientific, 1991); Verlinde E, Verlinde H "A Unitary S-Matrix for 2d Black Hole Formation and Evaporation" Preprint PUPT-1380, IASSNS-HEP-93/8 (1993), February
  113. Dijkgraaf R, Moore G, Plesser R "The Partition Function of 2D String Theory" Preprint IASSNS-HEP-92/48, YCTP-P22-92; Dijkgraaf R, Moore G, Plesser R "The Partition Function of 2D String Theory" hep-th/9208031, to appear in Nucl. Phys. B
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