Whitham deformations and Tau functions in N = 2 supersymmetric gauge theories

Progress of Theoretical Physics Supplement

Volumn , Issue 135, 1999, Pages 53-74

  Takasaki, Kanehisa ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235622     PISSN: 03759687     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTPS.135.53     Document Type: Article

References (92)

1. 1) N. Seiberg and E. Witten, Nucl. Phys. B426 (1994), 19; hep-th/9407087; Nucl. Phys. B431 (1994), 494; hep-th/9408099.
2. N. Seiberg and E. Witten, Nucl. Phys. B426 (1994), 19; hep-th/9407087; Nucl. Phys. B431 (1994), 494; hep-th/9408099.
3. A. Klemm, W. Lerche, S. Theisen and S. Yankielowicz, Phys. Lett. 344B (1995), 169; hep-th/9411048.
4. P. Argyres and A. Faraggi, Phys. Rev. Lett. 73 (1995), 3931; hep-th/9411057.
5. U. H. Danielsson and B. Sundborg, Phys. Lett. B358 (1995), 273; hep-th/9504102.
6. A. Hanany and Y. Oz, Nucl. Phys. B452 (1995), 283; hep-th/9505075.
7. A. Brandhuber and K. Landsteiner, Phys. Lett. B358 (1995), 73; hep-th/9507008.
8. P. C. Argyres and A. D. Shapere, Nucl. Phys. B461 (1996), 437; hep-th/9509175.
9. A. Hanany, Nucl. Phys. B466 (1996), 85; hep-th/9509176.
10. A. Gorsky, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. 335B (1995), 466; hep-th/9505035.
11. E. Martinec and N. P. Warner, Nucl. Phys. B459 (1996), 97; hep-th/9509161.
12. T. Nakatsu and K. Takasaki, Mod. Phys. Lett. A11 (1996), 157; hep-th/9509162.
13. R. Donagi and E. Witten, Nucl. Phys. B460 (1996), 299; hep-th/9510101.
14. T. Eguchi and S.-K. Yang, Mod. Phys. Lett. A11 (1996), 131; hep-th/9510183.
15. E. J. Martinec, Phys. Lett. B367 (1996), 91; hep-th/9510204.
16. A. Gorsky and A. Marshakov, Phys. Lett. B375 (1996), 127; hep-th/9510224.
17. H. Itoyama and A. Morozov, Nucl. Phys. B477 (1996), 855; hep-th/9511126; Nucl. Phys. B491 (1997), 529; hep-th/9512161.
18. H. Itoyama and A. Morozov, Nucl. Phys. B477 (1996), 855; hep-th/9511126; Nucl. Phys. B491 (1997), 529; hep-th/9512161.
19. A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B380 (1996), 75; hep-th/9603140; hep-th/9604078.
20. A. Marshakov, Mod. Phys. Lett. A11 (1996), 1169; hep-th/9602005; hep-th/9607159; Sakharov Conference 1996, p. 498; hep-th/9608161; Int. J. Mod. Phys. A12 (1997), 1607; hep-th/9610242.
21. A. Marshakov, Mod. Phys. Lett. A11 (1996), 1169; hep-th/9602005; hep-th/9607159; Sakharov Conference 1996, p. 498; hep-th/9608161; Int. J. Mod. Phys. A12 (1997), 1607; hep-th/9610242.
22. A. Marshakov, Mod. Phys. Lett. A11 (1996), 1169; hep-th/9602005; hep-th/9607159; Sakharov Conference 1996, p. 498; hep-th/9608161; Int. J. Mod. Phys. A12 (1997), 1607; hep-th/9610242.
23. C. Ahn and S. Nam, Phys. Lett. B387 (1996), 304; hep-th/9603028.
24. I. M. Krichever and D. H. Phong, J. Diff. Geom. 45 (1997), 349; hep-th/9604199.
25. N. Nekrasov, Nucl. Phys. B531 (1998), 323; hep-th/9609219.
26. E. D'Hoker, I. M. Krichever and D. H. Phong, Nucl. Phys. B494 (1997), 89; hep-th/9610156.
27. A. Gorsky, Phys. Lett. B410 (1997), 22; hep-th/9612238.
28. A. Marshakov, Theor. Math. Phys. 112 (1997), 791; hep-th/9702083.
29. A. Marshakov, M. Martellini and A. Morozov, Phys. Lett. B418 (1998), 294; hep-th/9706050.
30. A. Gorsky, S. Gukov and A. Mironov, Nucl. Phys. B517 (1998), 409; hep-th/9707120; Nucl. Phys. B518 (1998), 683; hep-th/9710239.
31. A. Gorsky, S. Gukov and A. Mironov, Nucl. Phys. B517 (1998), 409; hep-th/9707120; Nucl. Phys. B518 (1998), 683; hep-th/9710239.
32. E. D'Hoker and D. H. Phong, Nucl. Phys. B513 (1998), 405; hep-th/9709053.
33. A. Kapustin, Nucl. Phys. B545 (1998), 531; hep-th/9804069.
34. E. D'Hoker and D. H. Phong, Nucl. Phys. B530 (1998), 537: hep-th/9804126.
35. R. Donagi, Proc. Symp. Pure Math. (American Mathematical Society, Providence, 1997), vol. 62, Part 2, p. 3; alg-geom/9705010.
36. D. Freed, Commun. Math. Phys. 203 (1999), 31; hep-th/9712042.
37. M. Matone, Phys. Lett. B357 (1995), 342; hep-th/9506102.
38. J. Sonnenschein, S. Theisen and S. Yankielowicz, Phys. Lett. B367 (1996), 145; hep-th/9510129.
39. G. Bonelli and M. Matone, Phys. Rev. Lett. 76 (1996), 4107; hep-th/9602174.
40. A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, Nucl. Phys. B527 (1998), 690; hep-th/9802007.
41. K. Takasaki, Int. J. Mod. Phys. A14 (1999), 1001; hep-th/9803217.
42. J. D. Edelstein, M. Mariño and J. Mas, Nucl. Phys. B541 (1999), 671; hep-th/9805172.
43. J. D. Edelstein and J. Mas, Phys. Lett. B452 (1999), 69; hep-th/9901006.
44. K. Takasaki, hep-th/9901120.
45. J. D. Edelstein, M. Gómez-Reino and J. Mas, hep-th/9904087.
46. E. D'Hoker and D. H. Phong, hep-th/9903068.
47. A. Marshakov, hep-th/9903252.
48. M. Mariño, Prog. Theor. Phys. Suppl. No. 135 (1999), 29; hep-th/9905053.
49. G. Moore and E. Witten, Adv. Theor. Math. Phys. 1 (1998), 298; hep-th/9709193.
50. A. Losev, N. Nekrasov and S. Shatashvili, Nucl. Phys. B534 (1998), 549; hep-th/9711108; in Strings, Branes and Dualities, Cargèse, 1997, ed. L. Baulieu et al. (Kluwer Academic, Dordrecht, 1999), p. 359; hep-th/9801061.
51. A. Losev, N. Nekrasov and S. Shatashvili, Nucl. Phys. B534 (1998), 549; hep-th/9711108; in Strings, Branes and Dualities, Cargèse, 1997, ed. L. Baulieu et al. (Kluwer Academic, Dordrecht, 1999), p. 359; hep-th/9801061.
52. M. Mariño and G. Moore, Nucl. Phys. (Proc. Suppl.) 68 (1998), 336; hep-th/9712062; Commun. Math. Phys. 199 (1998), 25; hep-th/9802185.
53. M. Mariño and G. Moore, Nucl. Phys. (Proc. Suppl.) 68 (1998), 336; hep-th/9712062; Commun. Math. Phys. 199 (1998), 25; hep-th/9802185.
54. E. Date and S. Tanaka, Prog. Theor. Phys. 55 (1976), 457; Prog. Theor. Phys. Suppl. No. 59 (1976), 107.
55. E. Date and S. Tanaka, Prog. Theor. Phys. 55 (1976), 457; Prog. Theor. Phys. Suppl. No. 59 (1976), 107.
56. I. M. Krichever, Russ. Math. Surveys 33:4 (1978), 255.
57. P. van Moerbeke and D. Mumford, Acta Math. 143 (1979), 93.
58. M. Adler and P. van Moerbeke, Adv. in Math. 38 (1980), 267, 318.
59. R. Dijkgraaf, E. Verlinde and H. Verlinde, Nucl. Phys. B352 (1991), 59.
60. B. Blok and A. Varchenko, Int. J. Mod. Phys. A7 (1992), 1467.
61. G. Bonelli and M. Matone, Phys. Rev. Lett. 77 (1996), 4712; hep-th/9605090.
62. A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B389 (1996), 43; hep-th/9607109; Mod. Phys. Lett. A12 (1997), 773; hep-th/9701014.
63. A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B389 (1996), 43; hep-th/9607109; Mod. Phys. Lett. A12 (1997), 773; hep-th/9701014.
64. A. Mironov and A. Morozov, Phys. Lett. B424 (1998), 48; hep-th/9712177.
65. G. Bertoldi and M. Matone, Phys. Rev. D57 (1998), 6483; hep-th/9712109.
66. K. Ito and S.-K. Yang, Phys. Lett. B415 (1997), 45; hep-th/9708017; Phys. Lett. B433 (1998), 56; hep-th/9803126.
67. K. Ito and S.-K. Yang, Phys. Lett. B415 (1997), 45; hep-th/9708017; Phys. Lett. B433 (1998), 56; hep-th/9803126.
68. K. Ito, C.-S. Xiong and S.-K. Yang, Phys. Lett. B441 (1998), 155; hep-th/9807183.
69. J. Fay, Lecture Notes in Math. 352 (Springer Verlag, 1973).
70. B. A. Dubrovin, V. B. Matveev and S. P. Novikov, Russ. Math. Surveys 31:1 (1976), 59.
71. I. M. Krichever, Funct. Anal. Appl. 11 (1977), 12; Russ. Math. Surv. 32:6 (1977), 185.
72. I. M. Krichever, Funct. Anal. Appl. 11 (1977), 12; Russ. Math. Surv. 32:6 (1977), 185.
73. B. A. Dubrovin, Russ. Math. Surveys 36:2 (1981), 11.
74. M. Sato and Y. Sato, in Nonlinear Partial Differential Equations in Applied Sciences, ed. P. D. Lax , H. Fujita and G. Strang (North-Holland, Amsterdam, and Kinokuniya, Tokyo, 1982), p. 259.
75. E. Date, M. Kashiwara, M. Jimbo and T. Miwa, in Nonlinear Integrable Systems - Classical Theory and Quantum Theory, ed. M. Jimbo and T. Miwa (World Scientific, Singapore, 1983), p. 39.
76. G. Segal and G. Wilson, Publ. IHES 61 (1985), 5.
77. M. Mulase, J. Diff. Geom. 19 (1984), 403.
78. T. Shiota, Invent. Math. 83 (1986), 333.
79. K. Ueno and K. Takasaki, Adv. Stud. Pure. Math. (Kinokuniya, Tokyo, 1984), vol. 4, p. 1.
80. L. Alvarez-Gaumé, G. Moore and C. Vafa, Commun. Math. Phys. 106 (1986), 1.
81. N. Kawamoto, Y. Namikawa, A. Tsuchiya and Y. Yamada, Commun. Math. Phys. 116 (1988), 247.
82. D. Mumford, Tata lectures on theta (Birkhäuser, Boston, 1983).
83. E. Witten, Commun. Math. Phys. 117 (1988), 353.
84. S. K. Donaldson and P. B. Kronheimer, The geometry of four manifolds (Clarendon Press, Oxford, 1990).
85. R. Friedman and J. W. Morgan, Smooth four manifolds and complex surfaces (Springer-Verlag, 1991).
86. O. Ganor, Nucl. Phys. B488 (1997), 223; hep-th/9608109.
87. O. Ganor, D. R. Morrison and N. Seiberg, Nucl. Phys. 487 (1997), 93; hep-th/9610251.
88. W. Lerche, P. Mayr and N. P. Warner, Nucl. Phys. B499 (1997), 125; hep-th/9612085.
89. J. A. Minahan, D. Nemeschansky and N. P. Warner, Nucl. Phys. B508 (1997), 64; hep-th/9705237; Adv. Theor. Math. Phys. 1 (1998), 167; hep-th/9707149; Nucl. Phys. B528 (1998), 109; hep-th/9710146.
90. J. A. Minahan, D. Nemeschansky and N. P. Warner, Nucl. Phys. B508 (1997), 64; hep-th/9705237; Adv. Theor. Math. Phys. 1 (1998), 167; hep-th/9707149; Nucl. Phys. B528 (1998), 109; hep-th/9710146.
91. J. A. Minahan, D. Nemeschansky and N. P. Warner, Nucl. Phys. B508 (1997), 64; hep-th/9705237; Adv. Theor. Math. Phys. 1 (1998), 167; hep-th/9707149; Nucl. Phys. B528 (1998), 109; hep-th/9710146.
92. J. A. Minahan, D. Nemeschansky, C. Vafa and N. P. Warner, Nucl. Phys. B527 (1998), 581; hep-th/9802168.