M-theory of matrix models

Theoretical and Mathematical Physics

Volumn 150, Issue 2, 2007, Pages 153-164

  Alexandrov, A S ^a   Mironov, A D ^a,b   Morozov, A Yu ^a  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Duality; Matrix model; String theory

Indexed keywords

EID: 33847221176     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-007-0011-6     Document Type: Article

References (118)

1. A. Yu. Morozov, Sov. Phys. Usp., 35, 671 (1992).
2. 4 interaction," hep-th/0507129 (2005);
3. 4 term in the action beyond standard perturbative methods," hep-th/0503235 (2005);
4. V. Dolotin and A. Morozov, "Introduction to non-linear algebra," hep-th/0609022 (2006);
5. "Algebraic geometry of discrete dynamics: The case of one variable," hep-th/0501235 (2005).
6. S. Coleman, "The use of instantons," in: The Whys of Subnuclear Physics (Proc. Intl. School Subnuclear Physics, Erice, Sicily, 1977, A. Zichichi, ed.), Plenum, New York (1977), p. 805;
7. A. I. Vainshtein, V. I. Zakharov, V. A. Novikov, and M. A. Shifman, Sov. Phys. Usp., 25, 195 (1982);
8. P. Putrov, "Path integral in energy representation in quantum mechanics," hep-th/0605169 (2006).
9. N. A. Nekrasov, Adv. Theor. Math. Phys., 7, 831 (2004); hep-th/0206161 (2002);
10. R. Flume, R. Poghossian, and H. Storch, Modern Phys. Lett. A, 17, 327 (2002);
11. R. Flume and R. Poghossian, Internat. J. Mod. Phys. A, 18, 2541 (2003).
12. C. Callan, R. Dashen, and D. Gross, Phys. Rev. D, 17, 2717 (1978).
13. A. Mironov, A. Morozov, and T. Tomaras, JETP, 101, 331 (2005).
14. M. Atiyah, V. Drinfeld, N. Hitchin, and Yu. Manin, Phys. Lett. A, 65, 185 (1978).
15. A. Yu. Morozov, Sov. Phys. Usp., 37, 1 (1994);
16. "Matrix models as integrable systems," hep-th/9502091 (1995);
17. "Challenges of matrix models," hep-th/0502010 (2005);
18. A. Mironov, Internat. J. Mod. Phys. A, 9, 4355 (1994);
19. Phys. Part. Nucl., 33, 537 (2002).
20. A. Gerasimov, S. Khoroshkin, D. Lebedev, A. Mironov, and A. Morozov, Internat. J. Mod. Phys. A, 10, 2589 (1995);
21. A. Mironov, A. Morozov, and L. Vinet, Theor. Math. Phys., 100, 890 (1994);
22. S. Kharchev, A. Mironov, and A. Morozov, Theor. Math. Phys., 104, 866 (1995);
23. A. Mironov, "Quantum deformations of π-functions, bilinear identities, and representation theory," hep-th/9409190 (1994);
24. A. D. Mironov, Theor. Math. Phys., 114, 127 (1998).
25. A. Morozov, "Identities between quantum field theories in different dimensions," hep-th/9810031 (1998);
26. K. Saraikin, "Abelian varieties, RCFTs, attractors, and Hitchin functional in two dimensions," hep-th/0604176 (2006).
27. A. Alexandrov, A. Mironov, and A. Morozov, "Instantons and merons in matrix models," hep-th/0608228 (2006).
28. M. L. Kontsevich, Funct. Anal. Appl., 25, 123 (1991);
29. S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, and A. Zabrodin, Nucl. Phys. B, 380, 181 (1992);
30. Phys. Lett. B, 275, 311 (1992);
31. S. Kharchev, A. Marshakov, A. Mironov, and A. Morozov, Nucl. Phys. B, 397, 339 (1993);
32. Modern Phys. Lett. A, 8, 1047 (1993);
33. Internat. J. Mod. Phys. A, 10, 2015 (1995);
34. P. Di Francesco, C. Itzykson, and J.-B. Zuber, Comm. Math. Phys., 151, 193 (1993).
35. Yu. M. Makeenko, JETP Letters, 52, 259 (1990);
36. J. Ambjørn, J. Jurkiewicz, and Yu. Makeenko, Phys. Lett. B, 251, 517 (1990);
37. T. Morris, Nucl. Phys. B, 356, 703 (1991);
38. A. Anderson, R. C. Meyers, and V. Periwal, Phys. Lett. B, 254, 89 (1991).
39. Yu. Makeenko, A. Marshakov, A. Mironov, and A. Morozov, Nucl. Phys. B, 356, 574 (1991).
40. F. J. Dyson, J. Math. Phys., 3, 140 (1962);
41. M. L. Mehta, Random Matrices, Acad. Press, New York (1991);
42. E. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, Comm. Math. Phys., 59, 35 (1978);
43. D. Bessis, Comm. Math. Phys., 69, 147 (1979);
44. D. Bessis, C. Itzykson, and J.-B. Zuber, Adv. Appl. Math., 1, 109 (1980);
45. C. Itzykson and J.-B. Zuber, J. Math. Phys., 21, 411 (1980).
46. A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov, and A. Orlov, Nucl. Phys. B, 357, 565 (1991).
47. A. Alexandrov, A. Mironov, and A. Morozov, Internat. J. Mod. Phys. A, 19, 4127 (2004);
48. Fortschr. Phys., 53, 512 (2005);
49. A. S. Aleksandrov, A. D. Mironov, and A. Yu. Morozov, Theor. Math. Phys., 142, 349 (2005).
50. R. Dijkgraaf and C. Vafa, Nucl. Phys. B, 644, 3, 21 (2002); hep-th/0208048 (2002);
51. L. Chekhov and A. Mironov, Phys. Lett. B, 552, 293 (2003);
52. H. Itoyama and A. Morozov, Nucl. Phys. B, 657, 53 (2003);
53. Phys. Lett. B, 555, 287 (2003);
54. Progr. Theor. Phys., 109, 433 (2003);
55. Internat. J. Mod. Phys. A, 18, 5889 (2003);
56. L. Chekhov, A. Marshakov, A. Mironov, and D. Vasiliev, Phys. Lett. B, 562, 323 (2003);
57. L. O. Chekhov, A. V. Marshakov, A. D. Mironov, and D. Vasiliev, Proc. Steklov Math. Inst., 251, 254 (2005); hep-th/0506075 (2005).
58. A. Alexandrov, A. Mironov, and A. Morozov, Internat. J. Mod. Phys. A, 21, 2481 (2006); hep-th/0412099 (2004).
59. L. Chekhov, "Matrix models and geometry of moduli spaces," hep-th/9509001 (1995).
60. I. K. Kostov, "Conformal field theory techniques in random matrix models," hep-th/9907060 (1999).
61. G. Bonnet, F. David, and B. Eynard, J. Phys. A, 33, 6739 (2000);
62. A. Klemm, M. Mariño, and S. Theisen, JHEP, 0303, 051 (2003);
63. A. Givental, Internat. Math. Res. Notices, 2001, 1265 (2001); math.AG/0008067 (2000).
64. S. Kharchev and A. Marshakov, Internat. J. Mod. Phys. A, 10, 1219 (1995);
65. A. Mironov, "On GKM description of multi-criticality in 2d gravity," Preprint FIAN/TD/16-92, Lebedev Phys. Inst., Russ. Acad. Sci., Moscow (1992).
66. V. Periwal and D. Shevitz, Phys. Rev. Lett., 64, 1326 (1990);
67. Nucl. Phys. B, 344, 731 (1990);
68. M. Bowick, A. Morozov, and D. Shewitz, Nucl. Phys. B, 354, 496 (1991);
69. S. Kharchev and A. Mironov, Internat. J. Mod. Phys. A, 7, 4803 (1992);
70. A. Mironov, A. Morozov, and G. Semenoff, Internat. J. Mod. Phys. A, 10, 2015 (1995).
71. P. Horava and E. Witten, Nucl. Phys. B, 460, 506 (1996).
72. M. R. Douglas, JHEP, 0305, 046 (2003).
73. A. Gerasimov, D. Lebedev, and A. Morozov, Internat. J. Mod. Phys. A, 6, 977 (1991).
74. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, Phys. Rev. D, 55, 5112 (1997).
75. H. Weyl, Z. Phys., 46, 1 (1927);
76. H. Weyl, The Theory of Groups and Quantum Mechanics, Dover, New York (1931);
77. J. E. Moyal, Proc. Cambridge Phil. Soc., 45, 99 (1949).
78. I. A. Batalin and G. A. Vilkovisky, Phys. Lett. B, 102, 27 (1981);
79. Phys. Rev. D, 28, 2567 (1983);
80. Erratum, 30, 508 (1984);
81. I. A. Batalin and E. S. Fradkin, Phys. Lett. B, 122, 157 (1983);
82. B. L. Voronov and I. V. Tyutin, Theor. Math. Phys., 50, 218 (1982);
83. A. Schwarz, Comm. Math. Phys., 155, 249 (1993);
84. 158, 373 (1993);
85. A. Losev, V. Lysov, and A. Gorodentsev, "On BV and Berkovits theory," Report at Dombay Seminars on Berkovits Theory, Dombay (2003);
86. D. Krotov, A. Losev, and A. Gorodentsev, "Quantum field theory as effective BV theory from Chern-Simons," hep-th/0603201 (2006).
87. J. Ambjørn, L. Chekhov, and Yu. Makeenko, Phys. Lett. B, 282, 341 (1992);
88. J. Ambjørn, L. Chekhov, C. F. Kristjansen, and Yu. Makeenko, Nucl. Phys. B, 404, 127 (1993);
89. Erratum, 449, 681 (1995).
90. A. D. Mironov, Theor. Math. Phys., 146, 63 (2006).
91. H. Bateman and A. Erdélyi, eds., Higher Transcendental Functions (Based on notes left by H. Bateman), Vol. 2, McGraw-Hill, New York (1953).
92. I. M. Krichever and S. P. Novikov, Funct. Anal. Appl., 21, 126, 294 (1987);
93. 23, 19 (1989);
94. R. Dick, "Global expansions of holomorphic differentials on punctured Riemann surfaces," Preprint DESY-89-160, DESY, Hamburg (1989);
95. Lett. Math. Phys., 18, 255 (1989);
96. M. Schlichenmaier, Lett. Math. Phys., 19, 151, 327 (1990);
97. A. Ruffing, T. Deck, and M. Schlichenmaier, Lett. Math. Phys., 26, 23 (1992); hep-th/9207088 (1992);
98. A. Beilinson and V. Schechtman, Comm. Math. Phys., 118, 651 (1988);
99. A. Morozov, Phys. Lett. B, 196, 325 (1987).
100. V. G. Knizhnik and A. B. Zamolodchikov, Nucl. Phys. B, 247, 83 (1984).
101. N. Seiberg and E. Witten, Nucl. Phys. B, 426, 19 (1994);
102. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, and A. Morozov, Phys. Lett. B, 355, 466 (1995);
103. A. Marshakov, Seiberg-Witten Theory and Integrable Systems, World Scientific, Singapore (1999);
104. Integrability: The Seiberg-Witten and Whitham Equations, Gordon and Breach, Amsterdam (2000);
105. A. Gorsky and A. Mironov, "Integrable many-body systems and gauge theories," hep-th/0011197 (2000).
106. E. Witten, Nucl. Phys. B, 268, 253 (1986);
107. B. Zwiebach, Phys. Lett. B, 256, 22 (1991);
108. Modern Phys. Lett. A, 7, 1079 (1992);
109. Ann. Phys., 267, 193 (1998);
110. "Closed string field theory: An introduction," hep-th/9305026 (1993).
111. E. Witten, Nucl. Phys. B, 276, 291 (1986);
112. "Quantum background independence in string theory," hep-th/ 9306122 (1993);
113. A. Sen and B. Zwiebach, Nucl. Phys. B, 414, 649 (1994);
114. 423, 580 (1994);
115. Comm. Math. Phys., 177, 305 (1996);
116. A. Gerasimov and S. Shatashvili, JHEP, 0106, 066 (2001).
117. B. Eynard, JHEP, 0411, 031 (2004);
118. L. Chekhov and B. Eynard, JHEP, 0603, 014 (2006); hep-th/0504116 (2005).