Matrix models, complex geometry, and integrable systems: I

Theoretical and Mathematical Physics

Volumn 147, Issue 2, 2006, Pages 583-636

  Marshakov, A V ^a,b  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

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

Author keywords

Complex geometry; Matrix models; String theory

Indexed keywords

EID: 33646737651     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-006-0065-x     Document Type: Article

References (50)

1. A. M. Polyakov, Gauge Fields and Strings (Contemporary Concepts in Physics. Vol. 3), Harwood, Chur, Switzerland (1987).
2. J. Polchinski, Phys. Rev. Lett., 75, 4724 (1995); hep-th/9510017 (1995);
3. Progr. Theoret. Phys. (Suppl.), 123, 9 (1996); hep-th/9511157 (1995);
4. Rev. Modern Phys., 68, 1245 (1996); hep-th/9607050 (1996);
5. "TASI lectures on D-branes," hep-th/9611050 (1996).
6. J. Polchinski, String Theory, Vols. 1, 2, Cambridge Univ. Press, Cambridge (1998).
7. J. M. Maldacena, "TASI 2003 lectures on AdS/CFT," hep-th/0309246 (2003).
8. A. V. Marshakov, Phys. Usp., 45, 915 (2002); hep-th/0212114 (2002).
9. G. 't Hooft, Nucl. Phys. B, 72, 461 (1974).
10. E. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, Comm. Math. Phys., 59, 35 (1978);
11. F. David, Nucl. Phys. B, 257[FS14], 45 (1985);
12. V. Kazakov, Phys. Lett. B, 150, 282 (1985).
13. E. Witten, Comm. Math. Phys., 252, 189 (2004); hep-th/0312171 (2003);
14. Adv. Theor. Math. Phys., 8, 779 (2004); hep-th/0403199 (2004);
15. D. Polyakov, Phys. Lett. B, 611, 173 (2005); hep-th/0501219 (2005).
16. A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov, and A. Orlov, Nucl. Phys. B, 357, 565 (1991).
17. S. Kharchev, A. Marshakov, A. Mironov, A. Orlov, and A. Zabrodin, Nucl. Phys. B, 366, 569 (1991).
18. T. Miwa, Proc. Japan Acad. A, 58, 9 (1982).
19. S. Kharchev, A. Marshakov, A. Mironov, and A. Morozov, Nucl. Phys. B, 397, 339 (1993).
20. S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, and A. Zabrodin, Phys. Lett. B, 275, 311 (1992); hepth/9111037 (1991);
21. Nucl. Phys. B. 380, 181 (1992); hep-th/9201013 (1992).
22. M. Kontsevich, Funct. Anal. Appl., 25, 123 (1991);
23. Comm. Math, Phys., 147, 1 (1992).
24. M. Fukuma, H. Kawai, and R. Nakayama, Internat, J. Mod, Phys, A, 6, 1385 (1991);
25. Comm, Math. Phys., 143, 371 (1992).
26. S. Kharchev and A. Marshakov, "Topological versus non-topological theories and p-q duality in c≤1 2d gravity models," in: String Theory, Quantum Gravity, and the Unification of the Fundamental Interactions (Proc. Intl. Workshop on String Theory, Quantum Gravity, and the Unification of Fundamental Interactions, Rome, Italy, 1992, M. Bianchi, F. Fucito, E. Marinari, and A. Sagnotti, eds.), World Scientific, Singapore (1993), p. 331; hep-th/9210072 (1992);
27. Internat. J. Mod. Phys. A, 10, 1219 (1995); hep-th/9303100 (1993).
28. A. A. Migdal, Phys. Rep., 102, 199 (1983).
29. F. David, Phys. Lett. B, 302, 403 (1993); hep-th/9212106 (1992).
30. G. Bonnet, F. David, and B. Eynard, J. Phys. A, 33, 6739 (2000); cond-mat/0003324 (2000).
31. R. Dijkgraaf and C. Vafa, Nucl. Phys. B, 644, 3 (2002); hep-th/0206255 (2002);
32. Nucl. Phys. B, 644, 21 (2002); hep-th/0207106 (2002);
33. "A perturbative window into non-perturbative physics," hep-th/0208048 (2002).
34. G. Felder and R. Riser, Nucl. Phys. B, 691, 251 (2004); hep-th/0401191 (2004).
35. I. Krichever, Comm. Pure. Appl. Math., 47, 437 (1992); hep-th/9205110 (1992).
36. J. Fay, Theta-Functions on Riemann Surfaces (Lect. Notes Math., Vol. 352), Springer, Berlin (1973).
37. B. de Wit and A. V. Marshakov, Theor. Math. Phys., 129, 1504 (2001): hep-th/0105289 (2001).
38. L. Chekhov and A. Mironov, Phys. Lett. B, 552, 293 (2003); hep-th/0209085 (2002).
39. L. Chekhov, A. Marshakov, A. Mironov, and D. Vasiliev, Phys. Lett. B, 562, 323 (2003); hep-th/0301071 (2003).
40. V. A. Kazakov, A. Marshakov, J. A. Minahan, and K. Zarembo, JHEP, 0405, 024 (2004): hep-th/0402207 (2004);
41. A. V. Marshakov, Theor. Math. Phys., 142, 222 (2005); hep-th/0406056 (2004).
42. M. Mineev-Weinstein, P. B. Wiegmann, and A. Zabrodin, Phys. Rev. Lett., 84, 5106 (2000); nlin.SI/0001007 (2000):
43. K. Rostov, I. Krichever, M. Mineev-Weinstein, P. B. Wiegmann, and A. Zabrodin, "τ-Function for analytic curves," in: Random Matrices and Their Applications (Math. Sci. Res. Inst. Publ., Vol. 40, P. Bleher and A. Its, eds.), Cambridge Univ. Press, Cambridge (2001), p. 285; hep-th/0005259 (2000);
44. A. Zabrodin, "Matrix models and growth processes: From viscous flows to the quantum Hall effect," hep-th/0412219 (2004).
45. V. A. Kazakov and A. Marshakov, J. Phys. A, 36, 3107 (2003); hep-th/0211236 (2002).
46. B. Eynard, JHEP, 0301, 051 (2003): hep-th/0210047 (2002).
47. I. Krichever, A. Marshakov, and A. Zabrodin, Comm. Math. Phys., 259, 1 (2005); hep-th/0309010 (2003).
48. A. V. Marshakov, "Matrix models, complex geometry, and integrable systems: II," Theor. Math. Phys. (to appear); hep-th/0601214 (2006).
49. A. Marshakov, P. Wiegmann, and A. Zabrodin, Comm. Math. Phys., 227, 131 (2002); hep-th/0109048 (2001).
50. L. A. Takhtajan, Lett, Math. Phys., 56, 181 (2001); math.QA/0102164 (2001).