Complex curve of the two-matrix model and its tau-function

Journal of Physics A: Mathematical and General

Volumn 36, Issue 12 SPEC. ISS., 2003, Pages 3107-3136

  Kazakov, Vladimir A ^a   Marshakov, Andrei ^a,b,c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037471307     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/12/315     Document Type: Article

References (60)

1. Itzykson C and Zuber J-B 1980 The planar approximation II J. Math. Phys. 21 411 Mehta M-L 1981 A method of integration over matrix variables Commun. Math. Phys. 79 327
2. Itzykson C and Zuber J-B 1980 The planar approximation II J. Math. Phys. 21 411 Mehta M-L 1981 A method of integration over matrix variables Commun. Math. Phys. 79 327
3. Gerasimov A, Marshakov A, Mironov A, Morozov A and Orlov A 1991 Matrix models of 2D gravity and Toda theory Nucl. Phys. B 357 565
4. Kazakov V A 1986 Ising model on dynamical planar random lattice: exact solution Phys. Lett. A 119 140 Boulatov D V and Kazakov V A 1987 The Ising model on a random planar lattice: the structure of phase transition and the exact critical exponents Phys. Lett. B 186 379
5. Kazakov V A 1986 Ising model on dynamical planar random lattice: exact solution Phys. Lett. A 119 140 Boulatov D V and Kazakov V A 1987 The Ising model on a random planar lattice: the structure of phase transition and the exact critical exponents Phys. Lett. B 186 379
6. Kazakov V A 1989 The appearance of matter fields from quantum fluctuations of 2D-gravity Mod. Phys. Lett. A 4 2125
7. Douglas M R 1990 The two-matrix model Cargèse 1990, Proc. Random Surfaces and Quantum Gravity pp 77-83
8. Daul J-M, Kazakov V A and Kostov I K 1993 Rational theories of 2D gravity from the two-matrix model Nucl. Phys. B 409 311
9. Kharchev S and Marshakov A 1995 On p-q duality and explicit solutions in c ≤ 1 2-d gravity models Int. J. Mod. Phys. A 10 1219 (Preprint hep-th/9303100)
10. Mineev-Weinstein M, Wiegmann P B and Zabrodin A 2000 Integrable structure of interface dynamics Phys. Rev. Lett. 84 5106 (Preprint nlin.si/0001007)
11. Kostov I K, Krichever I, Mineev-Weinstein M, Wiegmann P B and Zabrodin A 2000 τ-function for analytic curves Preprint hep-th/0005259
12. Kazakov V A Unpublished; as cited in a footnote of [9]
13. Gorsky A, Krichever I, Marshakov A, Mironov A and Morozov A 1995 Integrability and Seiberg-Witten exact solution Phys. Lett. B 355 466 (Preprint hep-th/9505035)
14. Seiberg N and Witten E 1994 Monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory Nucl. Phys. B 426 19 (Preprint hep-th/9407087)
15. Gorsky A and Marshakov A 1996 Towards effective topological gauge theories on spectral curves Phys. Lett. B 375 127 (Preprinthep-th/9510224)
16. Nekrasov N A 2002 Seiberg-Witten prepotential from instanton counting Preprint hep-th/0206161
17. Marshakov A 1999 Seiberg-Witten Theory and Integrable Systems (Singapore: World Scientific) p 253
18. Krichever I M 1992 The tau function of the universal Whitham hierarchy, matrix models and topological field theories Commun. Pure. Appl. Math. 47 437 (Preprint hep-th/9205110)
19. David F 1993 Non-perturbative effects in matrix models and vacua of two dimensional gravity Phys. Lett. B 302 403-10 (Preprint hep-th/9212106) David F, Bonnet G, David F and Eynard B 2000 Breakdown of universality in multi-cut matrix models J. Phys. A: Math. Gen. 33 6739
20. David F 1993 Non-perturbative effects in matrix models and vacua of two dimensional gravity Phys. Lett. B 302 403-10 (Preprint hep-th/9212106) David F, Bonnet G, David F and Eynard B 2000 Breakdown of universality in multi-cut matrix models J. Phys. A: Math. Gen. 33 6739
21. Akemann G 1996 Higher genus correlators for the Hermitian matrix models with multiple cuts Nucl. Phys. 482 403 (Preprint hep-th/9606004)
22. Kostov I K 1999 Conformal field theory techniques in random matrix models Preprint hep-th/9907060
23. Dijkgraaf R and Vafa C 2002 Matrix models, topological strings, and supersymmetric gauge theories Preprint hep-th/0206255 Dijkgraaf R and Vafa C 2002 On geometry and matrix models Preprint hep-th/0207106 Dijkgraaf R and Vafa C 2002 A perturbative window into non-perturbative physics Preprint hep-th/0208048
24. Dijkgraaf R and Vafa C 2002 Matrix models, topological strings, and supersymmetric gauge theories Preprint hep-th/0206255 Dijkgraaf R and Vafa C 2002 On geometry and matrix models Preprint hep-th/0207106 Dijkgraaf R and Vafa C 2002 A perturbative window into non-perturbative physics Preprint hep-th/0208048
25. Dijkgraaf R and Vafa C 2002 Matrix models, topological strings, and supersymmetric gauge theories Preprint hep-th/0206255 Dijkgraaf R and Vafa C 2002 On geometry and matrix models Preprint hep-th/0207106 Dijkgraaf R and Vafa C 2002 A perturbative window into non-perturbative physics Preprint hep-th/0208048
26. Dijkgraaf R, Gukov S, Kazakov V A and Vafa C 2002 Perturbative analysis of gauged matrix models Preprint hep-th/0210238
27. Dorey N, Hollowood T J, Kumar S P and Sinkovics A 2002 Massive vacua of N = 1* theory and S-duality from matrix models Preprint hep-th/0209099
28. Chekhov L and Mironov A 2002 Matrix models vs. Seiberg-Witten/Whitham theories Preprint hep-th/0209085
29. Chau Ling-Lie and Zaboronsky O 1998 On the structure of normal matrix model Commun. Math. Phys. 196 203-47 (Preprint hep-th/9711091)
30. Wiegmann P B and Zabrodin A 2000 Conformal maps and dispersionless integrable hierarchies Commun. Math. Phys. 213 523 (Preprint hep-th/9909147)
31. Marshakov A, Wiegmann P and Zabrodin A 2002 Integrable structure of the Dirichlet boundary problem in two dimensions Commun. Math. Phys. 227 131 (Preprint hep-th/0109048)
32. Eynard B 2002 Large N expansion of the 2-matrix model Preprint hep-th/0210047
33. Kostov I K 1992 Gauge invariant matrix model for the A-D-E closed strings Phys. Lett. B 297 74 (Preprint hep-th/9208053)
34. Marshakov A, Mironov A and Morozov A 1991 Generalized matrix models as conformal field theories: discrete case Phys. Lett. B 265 99 Kharchev S, Marshakov A, Mironov A, Morozov A and Pakuliak S 1993 Conformal matrix models as an alternative to conventional multimatrix models Nucl. Phys. B 404 717 (Preprint hep-th/9208044)
35. Marshakov A, Mironov A and Morozov A 1991 Generalized matrix models as conformal field theories: discrete case Phys. Lett. B 265 99 Kharchev S, Marshakov A, Mironov A, Morozov A and Pakuliak S 1993 Conformal matrix models as an alternative to conventional multimatrix models Nucl. Phys. B 404 717 (Preprint hep-th/9208044)
36. Staudacher M 1993 Combinatorial solution of the two-matrix model Phys. Lett. B 305 332 (Preprint hep-th/9301038)
37. Boulatov D V 1993 Infinite tension strings at d > 1 Mod. Phys. Lett. A 8 557 (Preprint hep-th/9211064)
38. Krichever I 2000 unpublished
39. Ferrari F 2002 Quantum parameter space and double scaling limits in N = 1 super Yang-Mills theory Preprint hep-th/0211069
40. Migdal A A 1983 Loop equations and 1/N expansion Phys. Rep. 102 199
41. Dijkgraaf R, Grisaru M T, Lam C S, Vafa C and Zanon D 2002 Perturbative computation of glueball superpotentials Preprint hep-th/0211017
42. Cachazo F, Douglas M R, Seiberg N and Witten E 2002 Chiral rings and anomalies in supersymmetric gauge theory Preprint hep-th/0211170
43. Kazakov V A, Kostov I K and Nekrasov N A 1999 D-particles, matrix integrals and KP hierarchy Nucl. Phys. B 557 413 (Preprint hep-th/9810035) Goldstone J unpublished Hoppe J 1982 PhD Thesis MIT
44. Kazakov V A, Kostov I K and Nekrasov N A 1999 D-particles, matrix integrals and KP hierarchy Nucl. Phys. B 557 413 (Preprint hep-th/9810035) Goldstone J unpublished Hoppe J 1982 PhD Thesis MIT
45. Kazakov V A, Kostov I K and Nekrasov N A 1999 D-particles, matrix integrals and KP hierarchy Nucl. Phys. B 557 413 (Preprint hep-th/9810035) Goldstone J unpublished Hoppe J 1982 PhD Thesis MIT
46. Donagi R and Witten E 1996 Supersymmetric Yang-Mills theory and integrable systems Nucl. Phys. B 460 299 (Preprint hep-th/9510101)
47. Martinec E J 1996 Integrable structures in Supersymmetric gauge and string theory Phys. Lett. B 367 91 (Preprint hep-th/9510204)
48. Krichever I 1980 Func. Anal. Appl. 14 282
49. Aleksandrov S Yu, Kazakov V A and Kostov I K 2002 Time-dependent backgrounds of 2D string theory Nucl. Phys. B 640 119-44 (Preprint hep-th/0205079)
50. Kazakov V A 1988 Exactly solvable Potts models, bond and tree-like percolation on dynamical (random) planar lattice Nucl. Phys. B 4 (Proc. Suppl.) 93
51. Kazakov V A 2001 Solvable matrix models Random Matrices and Their Applications vol 40 MSRI publications (Preprint hep-th/0003064)
52. Cachazo F, Dijkgraaf R, Gukov S, Kazakov V A and Vafa C work in progress
53. Gopakumar R and Vafa C 1999 On the gauge theory/geometry correspondence Adv. Theor. Math. Phys. 3 1415-43 (Preprint hep-th/9811131)
54. Kazakov V A and Zinn-Justin P 1998 Two-matrix model with BABA interaction Preprint hep-th/9808043 Kazakov V A and Zinn-Justin P 1999 Nucl. Phys. B 546 647-68
55. Kazakov V A and Zinn-Justin P 1998 Two-matrix model with BABA interaction Preprint hep-th/9808043 Kazakov V A and Zinn-Justin P 1999 Nucl. Phys. B 546 647-68
56. Witten E 1990 On the structure of the topological phase of two-dimensional gravity Nucl. Phys. B 340 281 Dijkgraaf R, Verlinde H and Verlinde E 1991 Topological strings in D < 1 Nucl. Phys. B 352 59
57. Witten E 1990 On the structure of the topological phase of two-dimensional gravity Nucl. Phys. B 340 281 Dijkgraaf R, Verlinde H and Verlinde E 1991 Topological strings in D < 1 Nucl. Phys. B 352 59
58. Marshakov A, Mironov A and Morozov A 1996 WDVV-like equations in N = 2 SUSY Yang-Mills theory Phys. Lett. B 389 43 (Preprint hep-th/9607109)
59. Marshakov A 2002 On associativity equations Theor. Math. Phys. 132 895 (Tear. Mat. Fiz. 132 3) (Preprint hep-th/0201267)
60. Marshakov A 2002 On associativity equations Theor. Math. Phys. 132 895 (Tear. Mat. Fiz. 132 3) (Preprint hep-th/0201267)