Geometric engineering of quantum field theories

Nuclear Physics B

Volumn 497, Issue 1-2, 1997, Pages 173-195

  Katz, Sheldon ^a   Klemm, Albrecht ^b   Vafa, Cumrun ^c  

^a OKLAHOMA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

Local mirror symmetry; N = 2 supersymmetric Yang Mills theories; Type ii string compactification on Calabi Yau manifolds; World sheet and space time instantons

Indexed keywords

EID: 0031582557     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00282-4     Document Type: Article

References (59)

1. [1] E. Witten, String Theory Dynamics in Various Dimensions, Nucl. Phys. B 443 (1995) 85, hep-th/9503124, Some Comments On String Dynamics, Proc. String's 95, hep-th/9507121.
2. [2] A. Strominger, Nucl. Phys. B 452 (1995) 96, hep-th/9505105.
3. [3] B. Greene, D. Morrison and A. Strominger, Nucl. Phys. B 451 (1995) 109, hep-th/9504145.
4. [4] M. Bershadsky, V. Sadov and C. Vafa, Nucl. Phys. B 463 (1996) 398, hep-th/9510225.
5. [5] M. Bershadsky, V. Sadov and C. Vafa, Nucl. Phys. B 463 (1996) 420, hep-th/9511222.
6. [6] J. Polchinski, Dirichlet Branes and Ramond-Ramond Charges, Phys. Rev. Lett. 75 (1995) 4724, hep-th/9510017.
7. [7] A. Strominger and C. Vafa, Phys. Rev. Lett. 77 (1996) 2368.
8. [8] S. Kachru and C. Vafa, Nucl. Phys. B 450 (1995) 69, hep-th/9505105.
9. [9] S. Ferrara, J. Harvey, A. Strominger and C. Vafa, Phys. Lett. B 361 (1995) 59, hep-th/9505162.
10. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
11. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
12. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
13. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
14. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
15. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
16. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
17. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
18. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
19. [10] V. Kaplunovsky, J. Louis and S. Theisen, Phys. Lett. B 357 (1995) 71; A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313; C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050; I. Antoniadis, E. Gava, K. Narain and T. Taylor, Nucl. Phys. B 455 (1995) 109; B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, II, hep-th/9507151, hep-th 9507153; P. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233; I. Antoniadis, S. Ferrara and T. Taylor, Nucl. Phys. B 460 (1996) 489; G. Curio, Phys. Lett. B 366 (1996) 131; B 366(1996) 78; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
20. [11] A. Klemm, W. Lerche and P. Mayr, Phys. Lett. B 357 (1995) 313.
21. [12] C. Vafa and E. Witten, preprint HUTP-95-A023.
22. [13] S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, hep-th/9508155.
23. [14] A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, hep-th/9504034.
24. [15] S. Kachru and E. Silverstein, hep-th/9608194.
25. [16] P. Aspinwall, Phys. Lett. B 357 (1995) 329; B 371 (1996) 231.
26. [16] P. Aspinwall, Phys. Lett. B 357 (1995) 329; B 371 (1996) 231.
27. [17] S. Katz, D. Morrison and R. Plesser, hep-th/9601108.
28. [18] A. Klemm and P. Mayr, hep-th/9601014.
29. [19] P. Aspinwall and M. Gross, hep-th/9602118.
30. [20] M. Bershadsky, K. Intriligator, S. Kachru, D. Morrison, V. Sadov and C. Vafa, hep-th/9605200.
31. [21] P. Berglund, S. Katz, A. Klemm and P. Mayr, hep-th/9601108.
32. [22] S. Katz and C. Vafa, Nucl. Phys. B 497 (1997) 146 (in this issue), hep-th/9606086.
33. [23] E. Witten, Nucl. Phys. B 403 (1993) 159.
34. [24] P. Aspinwall, B. Greene, D. Morrison, Nucl. Phys. B 420 (1994) 184.
35. [25] A. Klemm, P. Mayr and C. Vafa, hep-th/9607139.
36. [26] N. Seiberg and E. Witten, Nucl. Phys. B 426 (1994) 19, hep-th/9407087.
37. [27] N. Seiberg and E. Witten, Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
38. [28] A. Klemm, S. Katz and C. Vafa, work in progress.
39. [29] B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. van Proeyen, Phys. Lett. B 134 (1984) 37; B. de Wit and A. van Proeyen, Nucl. Phys. B 245 (1984) 89; J.P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett. B 140 (1984) 307; B. de Wit, P.G. Lauwers and A. van Proeyen, Nucl. Phys. B 255 (1985) 569; E. Cremmer, C. Kounnas, A. van Proeyen, J.P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B 250 (1985) 385.
40. [29] B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. van Proeyen, Phys. Lett. B 134 (1984) 37; B. de Wit and A. van Proeyen, Nucl. Phys. B 245 (1984) 89; J.P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett. B 140 (1984) 307; B. de Wit, P.G. Lauwers and A. van Proeyen, Nucl. Phys. B 255 (1985) 569; E. Cremmer, C. Kounnas, A. van Proeyen, J.P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B 250 (1985) 385.
41. [29] B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. van Proeyen, Phys. Lett. B 134 (1984) 37; B. de Wit and A. van Proeyen, Nucl. Phys. B 245 (1984) 89; J.P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett. B 140 (1984) 307; B. de Wit, P.G. Lauwers and A. van Proeyen, Nucl. Phys. B 255 (1985) 569; E. Cremmer, C. Kounnas, A. van Proeyen, J.P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B 250 (1985) 385.
42. [29] B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. van Proeyen, Phys. Lett. B 134 (1984) 37; B. de Wit and A. van Proeyen, Nucl. Phys. B 245 (1984) 89; J.P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett. B 140 (1984) 307; B. de Wit, P.G. Lauwers and A. van Proeyen, Nucl. Phys. B 255 (1985) 569; E. Cremmer, C. Kounnas, A. van Proeyen, J.P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B 250 (1985) 385.
43. [29] B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. van Proeyen, Phys. Lett. B 134 (1984) 37; B. de Wit and A. van Proeyen, Nucl. Phys. B 245 (1984) 89; J.P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett. B 140 (1984) 307; B. de Wit, P.G. Lauwers and A. van Proeyen, Nucl. Phys. B 255 (1985) 569; E. Cremmer, C. Kounnas, A. van Proeyen, J.P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B 250 (1985) 385.
44. [30] N. Berkovits and W. Siegel, Nucl. Phys. B 462 (1996) 213.
45. [31] C. Vafa and E. Witten, Nucl. Phys. B 447 (1995) 261.
46. [32] M. Duff and R. Khuri, Nucl. Phys. B 411 (1994) 473; C.M. Hull and P.K. Townsend, Nucl. Phys. B 438 (1995) 109.
47. [32] M. Duff and R. Khuri, Nucl. Phys. B 411 (1994) 473; C.M. Hull and P.K. Townsend, Nucl. Phys. B 438 (1995) 109.
48. [33] P. Candelas, X. de la Ossa, P. Green and L. Parkes, Nucl. Phys. B 359 (1991) 21.
49. [34] D. Morrison and R. Plesser, Nucl. Phys. B 440 (1995) 279, hep-th/9412236, Towards Mirror Symmetry as Duality For Two-Dimensional Abelian Gauge Theories, hep-th/9508107.
50. [35] V. Batyrev, Duke Math. J. 69 (1993) 349; J. Alg. Geom. 3 (1994) 493; Quantum Cohomology Rings of Toric Manifolds, preprint 1992; V. Batyrev and A. Borisov, alg-geom/9412017, alg-geom/9509009.
51. [35] V. Batyrev, Duke Math. J. 69 (1993) 349; J. Alg. Geom. 3 (1994) 493; Quantum Cohomology Rings of Toric Manifolds, preprint 1992; V. Batyrev and A. Borisov, alg-geom/9412017, alg-geom/9509009.
52. [35] V. Batyrev, Duke Math. J. 69 (1993) 349; J. Alg. Geom. 3 (1994) 493; Quantum Cohomology Rings of Toric Manifolds, preprint 1992; V. Batyrev and A. Borisov, alg-geom/9412017, alg-geom/9509009.
53. [35] V. Batyrev, Duke Math. J. 69 (1993) 349; J. Alg. Geom. 3 (1994) 493; Quantum Cohomology Rings of Toric Manifolds, preprint 1992; V. Batyrev and A. Borisov, alg-geom/9412017, alg-geom/9509009.
54. [36] S. Hosono. A. Klemm, S. Theisen and S.-T. Yau, Comm. Math. Phys. 167 (1995) 301.
55. [37] S. Katz, M. Douglas and C. Vafa, hep-th/9609071.
56. [38] A. Gorskii, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 355 (1995) 466; H. Itoyama and A. Morozov, hep-th/9511126; hep-th/9512161; E. Martinec and N. Warner, Nucl. Phys. B 459 (1996) 97.
57. [38] A. Gorskii, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 355 (1995) 466; H. Itoyama and A. Morozov, hep-th/9511126; hep-th/9512161; E. Martinec and N. Warner, Nucl. Phys. B 459 (1996) 97.
58. [38] A. Gorskii, I. Krichever, A. Marshakov, A. Mironov and A. Morozov, Phys. Lett. B 355 (1995) 466; H. Itoyama and A. Morozov, hep-th/9511126; hep-th/9512161; E. Martinec and N. Warner, Nucl. Phys. B 459 (1996) 97.
59. [39] A. Klemm, W. Lerche and S. Theisen, Int. J. Mod. Phys. A 11 (1996) 1929, hep-th/9505150.