Whitham hierarchies, instanton corrections and soft supersymmetry breaking in N = 2 SU (N) super Yang-Mills theory

Nuclear Physics B

Volumn 541, Issue 3, 1999, Pages 671-697

  Edelstein, José D ^a   Mariño, Marcos ^b   Mas, Javier ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b Yale University   (United States)

Author keywords

Instanton corrections; Seiberg Witten solution; Soft supersymmetry breaking; Supersymmetric gauge theories; Whitham hierarchies

Indexed keywords

EID: 0033099948     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00798-6     Document Type: Article

References (64)

1. [1] N. Seiberg and E. Witten, Nucl. Phys. B 426 (1994) 19; B 430 (1994) 485 (E), hep-th/9407087; Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
2. [1] N. Seiberg and E. Witten, Nucl. Phys. B 426 (1994) 19; B 430 (1994) 485 (E), hep-th/9407087; Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
3. [1] N. Seiberg and E. Witten, Nucl. Phys. B 426 (1994) 19; B 430 (1994) 485 (E), hep-th/9407087; Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
4. [2] A. Klemm, W. Lerche, S. Theisen and S. Yankielowicz, Phys. Lett. B 344 (1995) 169, hep-th/9411048; P.C. Argyres and A.E. Faraggi, Phys. Rev. Lett. 74 (1995) 3931, hep-th/9411057.
5. [2] A. Klemm, W. Lerche, S. Theisen and S. Yankielowicz, Phys. Lett. B 344 (1995) 169, hep-th/9411048; P.C. Argyres and A.E. Faraggi, Phys. Rev. Lett. 74 (1995) 3931, hep-th/9411057.
6. [3] L. Girardello and M.T. Grisaru, Nucl. Phys. B 194 (1982) 65.
7. [4] L. Álvarez-Gaumé, J. Distler, C. Kounnas and M. Mariño, Int. J. Mod. Phys. A 11 (1996) 4745, hep-th/9604004.
8. [5] L. Álvarez-Gaumé and M. Mariño, Int. J. Mod. Phys. A 12 (1997) 975, hep-th/9606191.
9. [6] L. Alvarez-Gaumé, M. Mariño and F. Zamora, Int. J. Mod. Phys. A 13 (1998) 403, hep-th/9703072; Int. J. Mod. Phys. A 13 (1998) 1847, hep-th/9707017; M. Mariño and F. Zamora, Nucl. Phys. B, in press, hep-th/9804038.
10. [6] L. Alvarez-Gaumé, M. Mariño and F. Zamora, Int. J. Mod. Phys. A 13 (1998) 403, hep-th/9703072; Int. J. Mod. Phys. A 13 (1998) 1847, hep-th/9707017; M. Mariño and F. Zamora, Nucl. Phys. B, in press, hep-th/9804038.
11. [6] L. Alvarez-Gaumé, M. Mariño and F. Zamora, Int. J. Mod. Phys. A 13 (1998) 403, hep-th/9703072; Int. J. Mod. Phys. A 13 (1998) 1847, hep-th/9707017; M. Mariño and F. Zamora, Nucl. Phys. B, in press, hep-th/9804038.
12. [7] N. Evans, S.D.H. Hsu and M. Schwetz, Nucl. Phys. B 484 (1997) 124, hep-th/9608135.
13. [8] R. Dijkgraaf, H. Verlinde and E. Verlinde, Nucl. Phys. B 352 (1991) 59; I. Krichever, Comm. Math. Phys. 143 (1992) 415; B.A. Dubrovin, Comm. Math. Phys. 145 (1992) 195; B. Block and A. Varchenko, Int. J. Mod. Phys. A 7 (1992) 1467.
14. [8] R. Dijkgraaf, H. Verlinde and E. Verlinde, Nucl. Phys. B 352 (1991) 59; I. Krichever, Comm. Math. Phys. 143 (1992) 415; B.A. Dubrovin, Comm. Math. Phys. 145 (1992) 195; B. Block and A. Varchenko, Int. J. Mod. Phys. A 7 (1992) 1467.
15. [8] R. Dijkgraaf, H. Verlinde and E. Verlinde, Nucl. Phys. B 352 (1991) 59; I. Krichever, Comm. Math. Phys. 143 (1992) 415; B.A. Dubrovin, Comm. Math. Phys. 145 (1992) 195; B. Block and A. Varchenko, Int. J. Mod. Phys. A 7 (1992) 1467.
16. [8] R. Dijkgraaf, H. Verlinde and E. Verlinde, Nucl. Phys. B 352 (1991) 59; I. Krichever, Comm. Math. Phys. 143 (1992) 415; B.A. Dubrovin, Comm. Math. Phys. 145 (1992) 195; B. Block and A. Varchenko, Int. J. Mod. Phys. A 7 (1992) 1467.
17. [9] A. Gorsky, I.M. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 355 (1995) 466, hep-th/9505035.
18. [10] E. Martinec and N.P. Warner, Nucl. Phys. B 459 (1996) 97, hep-th/9509161; T. Nakatsu and K. Takasaki, Mod. Phys. Lett. A 11 (1996) 157, hep-th/9509162; H. Itoyama and A. Morozov, Nucl. Phys. B 477 (1996) 855, hep-th/9511126; B 491 (1997) 529, hep-th/9512161.
19. [10] E. Martinec and N.P. Warner, Nucl. Phys. B 459 (1996) 97, hep-th/9509161; T. Nakatsu and K. Takasaki, Mod. Phys. Lett. A 11 (1996) 157, hep-th/9509162; H. Itoyama and A. Morozov, Nucl. Phys. B 477 (1996) 855, hep-th/9511126; B 491 (1997) 529, hep-th/9512161.
20. [10] E. Martinec and N.P. Warner, Nucl. Phys. B 459 (1996) 97, hep-th/9509161; T. Nakatsu and K. Takasaki, Mod. Phys. Lett. A 11 (1996) 157, hep-th/9509162; H. Itoyama and A. Morozov, Nucl. Phys. B 477 (1996) 855, hep-th/9511126; B 491 (1997) 529, hep-th/9512161.
21. [10] E. Martinec and N.P. Warner, Nucl. Phys. B 459 (1996) 97, hep-th/9509161; T. Nakatsu and K. Takasaki, Mod. Phys. Lett. A 11 (1996) 157, hep-th/9509162; H. Itoyama and A. Morozov, Nucl. Phys. B 477 (1996) 855, hep-th/9511126; B 491 (1997) 529, hep-th/9512161.
22. [11] G. Moore and E. Witten, Adv. Theor. Math. Phys. 1 (1997) 298, hep-th/9709193.
23. [12] M. Mariño and G. Moore, Nucl. Phys. Proc. Suppl. 68 (1998) 336, hep-th/9712062.
24. [13] M. Mariño and G. Moore, hep-th/9802185.
25. [14] M. Mariño and G. Moore, hep-th/9804104.
26. [15] A. Losev, N. Nekrasov and S. Shatashvili, hep-th/9711108; hep-th/9801061.
27. [16] K. Takasaki, hep-th/9803217.
28. [17] A. Gorsky, A. Marshakov, A. Mironov and A. Morozov, Nucl. Phys. B 527 (1998) 690, hep-th/9802007.
29. [18] M. Matone, Phys. Lett. B 357 (1995) 342, hep-th/9506102.
30. [19] J. Sonnenschein, S. Theisen and S. Yankielowicz, Phys. Lett. B 367 (1996) 145, hep-th/9510129; T. Eguchi and S-K. Yang, Mod. Phys. Lett. A 11 (1996) 131, hep-th/9510183; E. D'Hoker, I.M. Krichever and D.H. Phong, Nucl. Phys. B 494 (1997) 89, hep-th/9610156.
31. [19] J. Sonnenschein, S. Theisen and S. Yankielowicz, Phys. Lett. B 367 (1996) 145, hep-th/9510129; T. Eguchi and S-K. Yang, Mod. Phys. Lett. A 11 (1996) 131, hep-th/9510183; E. D'Hoker, I.M. Krichever and D.H. Phong, Nucl. Phys. B 494 (1997) 89, hep-th/9610156.
32. [19] J. Sonnenschein, S. Theisen and S. Yankielowicz, Phys. Lett. B 367 (1996) 145, hep-th/9510129; T. Eguchi and S-K. Yang, Mod. Phys. Lett. A 11 (1996) 131, hep-th/9510183; E. D'Hoker, I.M. Krichever and D.H. Phong, Nucl. Phys. B 494 (1997) 89, hep-th/9610156.
33. [20] N. Evans and M. Schwetz, Nucl. Phys. B 522 (1998) 69, hep-th/9708122; N. Evans, hep-th/9801159; hep-th/9804097; J.L.F. Barbón and A. Pasquinucci, Phys. Lett. B 421 (1998) 131, hep-th/9711030; Mod. Phys. Lett. A 13 (1998) 1453, hep-th/9804029.
34. [20] N. Evans and M. Schwetz, Nucl. Phys. B 522 (1998) 69, hep-th/9708122; N. Evans, hep-th/9801159; hep-th/9804097; J.L.F. Barbón and A. Pasquinucci, Phys. Lett. B 421 (1998) 131, hep-th/9711030; Mod. Phys. Lett. A 13 (1998) 1453, hep-th/9804029.
35. [20] N. Evans and M. Schwetz, Nucl. Phys. B 522 (1998) 69, hep-th/9708122; N. Evans, hep-th/9801159; hep-th/9804097; J.L.F. Barbón and A. Pasquinucci, Phys. Lett. B 421 (1998) 131, hep-th/9711030; Mod. Phys. Lett. A 13 (1998) 1453, hep-th/9804029.
36. [20] N. Evans and M. Schwetz, Nucl. Phys. B 522 (1998) 69, hep-th/9708122; N. Evans, hep-th/9801159; hep-th/9804097; J.L.F. Barbón and A. Pasquinucci, Phys. Lett. B 421 (1998) 131, hep-th/9711030; Mod. Phys. Lett. A 13 (1998) 1453, hep-th/9804029.
37. [21] A. Gorsky, Phys. Lett. B 410 (1997) 22, hep-th/9612238; A. Gorsky, S. Gukov and A. Mironov, Nucl. Phys. B 517 (1998) 409, hep-th/9707120.
38. [21] A. Gorsky, Phys. Lett. B 410 (1997) 22, hep-th/9612238; A. Gorsky, S. Gukov and A. Mironov, Nucl. Phys. B 517 (1998) 409, hep-th/9707120.
39. [22] R. Carroll, hep-th/9802130; hep-th/9804086.
40. [23] D. Mumford, Tata Lectures on Theta (Birkhaüser, Basel, 1983).
41. [24] H.E. Rauch and H.M. Farkas, Theta functions with applications to Riemann surfaces, Williams and Wilkins, 1974.
42. [25] A. Klemm, W. Lerche and S. Theisen, Int. J. Mod. Phys. A 11 (1996) 1929, hep-th/9505150.
43. [26] K. Ito and S.K. Yang, Phys. Lett. B 366 ( 1996) 165, hep-th/9507144.
44. [27] E. D'Hoker, I.M. Krichever and D.H. Phong, Nucl. Phys. B 489 (1997) 179, hep-th/9609041; Nucl. Phys. B 489 (1997) 211, hep-th/9609145.
45. [27] E. D'Hoker, I.M. Krichever and D.H. Phong, Nucl. Phys. B 489 (1997) 179, hep-th/9609041; Nucl. Phys. B 489 (1997) 211, hep-th/9609145.
46. [28] K. Ito and S.-K. Yang, hep-th/9712018.
47. [29] S.G. Naculich, H. Rhedin and H.J. Schnitzer, hep-th/9804105; I.P. Ennes, S.G. Naculich, H. Rhedin and H.J. Schnitzer, hep-th/9804151.
48. [29] S.G. Naculich, H. Rhedin and H.J. Schnitzer, hep-th/9804105; I.P. Ennes, S.G. Naculich, H. Rhedin and H.J. Schnitzer, hep-th/9804151.
49. [30] D. Finnel and P. Pouliot, Nucl. Phys. B 453 (1995) 225, hep-th/9503115; A. Yung, Nucl. Phys. B 485 (1997) 38, hep-th/9605096; F. Fucito and G. Travaglini, Phys. Rev. D 55 (1997) 1099, hep-th/9605215; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Lett. B 390 (1997) 205, hep-th/9606199; T. Harano and M. Sato, Nucl. Phys. B 484 (1997) 167, hep-th/9608060.
50. [30] D. Finnel and P. Pouliot, Nucl. Phys. B 453 (1995) 225, hep-th/9503115; A. Yung, Nucl. Phys. B 485 (1997) 38, hep-th/9605096; F. Fucito and G. Travaglini, Phys. Rev. D 55 (1997) 1099, hep-th/9605215; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Lett. B 390 (1997) 205, hep-th/9606199; T. Harano and M. Sato, Nucl. Phys. B 484 (1997) 167, hep-th/9608060.
51. [30] D. Finnel and P. Pouliot, Nucl. Phys. B 453 (1995) 225, hep-th/9503115; A. Yung, Nucl. Phys. B 485 (1997) 38, hep-th/9605096; F. Fucito and G. Travaglini, Phys. Rev. D 55 (1997) 1099, hep-th/9605215; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Lett. B 390 (1997) 205, hep-th/9606199; T. Harano and M. Sato, Nucl. Phys. B 484 (1997) 167, hep-th/9608060.
52. [30] D. Finnel and P. Pouliot, Nucl. Phys. B 453 (1995) 225, hep-th/9503115; A. Yung, Nucl. Phys. B 485 (1997) 38, hep-th/9605096; F. Fucito and G. Travaglini, Phys. Rev. D 55 (1997) 1099, hep-th/9605215; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Lett. B 390 (1997) 205, hep-th/9606199; T. Harano and M. Sato, Nucl. Phys. B 484 (1997) 167, hep-th/9608060.
53. [30] D. Finnel and P. Pouliot, Nucl. Phys. B 453 (1995) 225, hep-th/9503115; A. Yung, Nucl. Phys. B 485 (1997) 38, hep-th/9605096; F. Fucito and G. Travaglini, Phys. Rev. D 55 (1997) 1099, hep-th/9605215; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Lett. B 390 (1997) 205, hep-th/9606199; T. Harano and M. Sato, Nucl. Phys. B 484 (1997) 167, hep-th/9608060.
54. [31] M.J. Slater, Phys. Lett. B 403 (1997) 57, hep-th/9701170; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Rev. D 54 (1996) 2921, hep-th/9603136; K. Ito and N. Sasakura, Phys. Lett. B 382 (1996) 95, hep-th/9602073; Nucl. Phys. B 484 (1997) 141, hep-th/9608054.
55. [31] M.J. Slater, Phys. Lett. B 403 (1997) 57, hep-th/9701170; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Rev. D 54 (1996) 2921, hep-th/9603136; K. Ito and N. Sasakura, Phys. Lett. B 382 (1996) 95, hep-th/9602073; Nucl. Phys. B 484 (1997) 141, hep-th/9608054.
56. [31] M.J. Slater, Phys. Lett. B 403 (1997) 57, hep-th/9701170; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Rev. D 54 (1996) 2921, hep-th/9603136; K. Ito and N. Sasakura, Phys. Lett. B 382 (1996) 95, hep-th/9602073; Nucl. Phys. B 484 (1997) 141, hep-th/9608054.
57. [31] M.J. Slater, Phys. Lett. B 403 (1997) 57, hep-th/9701170; N. Dorey, V.V. Khoze, and M.P. Mattis, Phys. Rev. D 54 (1996) 2921, hep-th/9603136; K. Ito and N. Sasakura, Phys. Lett. B 382 (1996) 95, hep-th/9602073; Nucl. Phys. B 484 (1997) 141, hep-th/9608054.
58. [32] V.V. Khoze, M.P. Mattis and M.J. Slater, hep-th/9804009.
59. [33] J.A. Minahan, D. Nemeschansky and N.P. Warner, Nucl. Phys. B 528 (1998) 109, hep-th/9710146.
60. [34] P.C. Argyres and M.R. Douglas, Nucl. Phys. B 448 (1995) 93, hep-th/9505062.
61. [35] D. Kutasov, A. Schwimmer and N. Seiberg, Nucl. Phys. B 459 (1996) 455, hep-th/9510222.
62. [36] M.R. Douglas and S.H. Shenker, Nucl. Phys. B 447 (1995) 271, hep-th/9503163.
63. [37] T. Masuda and H. Suzuki, Nucl. Phys. B 495 (1997) 149, hep-th/9612240.
64. [38] T. Kubota and N. Yokoi, hep-th/9712054.