On four-dimensional compactifications of F-theory

Nuclear Physics B

Volumn 505, Issue 1-2, 1997, Pages 165-201

  Bershadsky, Michael ^a   Johansen, Andrei ^a   Pantev, Tony ^b   Sadov, Vladimir ^c  

^a HARVARD UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Duality; Gauge; Geometry; String; Supersymmetry

Indexed keywords

EID: 0031563994     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00393-3     Document Type: Article

References (48)

1. [1] D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds-I, II, Nucl. Phys. B 473 (1996) 74; B 476 (1996) 437.
2. [1] D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds-I, II, Nucl. Phys. B 473 (1996) 74; B 476 (1996) 437.
3. [2] M. Bershadsky, K. Intriligator, S. Kachru, D. Morrison, V. Sadov and C. Vafa, Geometric Singularities and Enhanced Gauge Symmetries, Nucl. Phys. B 481 (1996) 215.
4. [3] C. Vafa and E. Witten, Nucl. Phys. B 447 (1995) 261.
5. [4] K. Becker and M. Becker, Nucl. Phys. B 477 (1996) 155.
6. [5] S. Sethi, C. Vafa and E. Witten, Nucl. Phys. B 480 (1996) 213.
7. [6] E. Witten, On flux quantization in M-theory and the effective action, hep-th/9609122.
8. [7] E. Witten, unpublished.
9. [8] T. Banks, M. Douglas and N. Seiberg, Phys. Lett. B 387 (1996) 278.
10. [9] E. Witten, Nucl. Phys. B 460 (1996) 335.
11. [10] A. Sen, BPS States on a Three Brane Probe, hep th/9608005.
12. [11] E. Witten, Small Instantons in String Theory, Nucl. Phys. B 460 (1996) 541.
13. [12] M. Douglas, Gauge Fields and D-branes, hep-th/9604198.
14. [13] See, for example, R. Donagi, Spectral covers, in Current topics in complex algebraic geometry (Berkeley, CA, 1992/93), 65-86, MSRI Publ. 28 and R. Donagi and E. Markman Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles in Integrable systems and quantum groups (Montecatini Terme, 1993), 1-119, LNM 1620, and references therein.
15. [13] See, for example, R. Donagi, Spectral covers, in Current topics in complex algebraic geometry (Berkeley, CA, 1992/93), 65-86, MSRI Publ. 28 and R. Donagi and E. Markman Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles in Integrable systems and quantum groups (Montecatini Terme, 1993), 1-119, LNM 1620, and references therein.
16. [14] R. Friedman, J. Morgan and E. Witten, Vector Bundles and F Theory, hep-th/9701162.
17. [15] I. Brunner and R. Schimmrigk, F-Theory on Calabi-Yau Fourfolds, Phys. Lett. B 387 (1996) 750.
18. [16] M. Bianchi, S. Ferrara, G. Pradisi, A. Sagnotti and Ya.S. Stanev, Twelve-Dimensional Aspects of Four-Dimensional N = 1 Type I Vacua, Phys. Lett. B 387 (1996) 64.
19. [17] S. Kachru and E. Silverstein, Singularities, Gauge Dynamics, and Non-perturbative Superpotentials in String Theory, hep-th/9608194.
20. [18] P. Mayr, Mirror Symmetry, N = 1 Superpotentials and Tensionless Strings on Calabi-Yau Fourfolds, hep-th/9610162.
21. [19] I. Brunner, M. Lynker and R. Schimmrigk, Unification of M-and F-Theory Calabi-Yau Fourfold Vacua, hep-th/9610195.
22. [20] S. Katz and C. Vafa, Geometric Engineering of N = 1 Quantum Field Theories, hep-th/9611090.
23. [21] M. Bershadsky, A. Johansen, T. Pantev, V. Sadov and C. Vafa, F-theory, Geometric Engineering and N = 1 Dualities, hep-th/9612052.
24. [22] C. Vafa and B. Zwiebach, N = 1 Dualities of SO and USp Gauge Theories and T-Duality of String Theory, hep-th/9701015.
25. [23] A. Klemm, B. Lian, S.-S. Roan and S.-T. Yau, Calabi-Yau fourfolds for M-and F-theory compactifications, hep-th/9701023.
26. [24] C. Vafa and E. Witten, Dual String Pairs with N = 1 and N = 2 Supersymmetry In Four Dimensions, hep-th/9507050.
27. [25] K. Narain, Phys. Lett. B 169 (1986) 41; K. Narain, H. Sarmadi and E. Witten, Nucl. Phys. B 279 (1991) 526.
28. [25] K. Narain, Phys. Lett. B 169 (1986) 41; K. Narain, H. Sarmadi and E. Witten, Nucl. Phys. B 279 (1991) 526.
29. [26] M. Bershadsky, V. Sadov and C. Vafa, D-branes and Topological Field Theories, Nucl. Phys. B 463 (1996) 420.
30. [27] E. Witten, Nucl. Phys. B 443 (1995) 85.
31. [28] P. Aspinwall and D. Morrison, Phys. Lett. B 355 (1995) 141.
32. [29] M. Bershadsky, A. Johansen, T. Pantev and V. Sadov, work in progress.
33. [30] Ron Donagi, Lawrence Ein and Robert Lazarsfeld, A non-linear deformation of the Hitchin dynamical system, alg-geom/9504017.
34. [31] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular Functions of One Variable IV, Lecture Notes in Math., Vol. 476 (Springer, Berlin, 1975).
35. [32] C. Vafa, Nucl. Phys. B 469 (1996) 403.
36. [33] E. Witten, Non-perturbative superpotentials in String Theory, Nucl. Phys. B 474 (1996) 343.
37. [34] O. Aharony, S. Kachru and E. Silverstein, New N = 1 Superconformal Field Theories in Four Dimensions from D-brane Probes, hep-th/9610205.
38. [35] I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B 241 (1984) 493; Nucl. Phys. B 256 (1985) 557.
39. [35] I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B 241 (1984) 493; Nucl. Phys. B 256 (1985) 557.
40. [36] S. Kachru, N. Seiberg and E. Silverstein, SUSY Gauge Dynamics and Singularities of 4D N = 1 String Vacua, Nucl. Phys. B 480 (1996) 170.
41. [37] M. Bershadsky and A. Johansen, Colliding Singularities in F-theory and Phase Transitions, Nucl. Phys. B 489 (1997) 122, hep-th/9610111.
42. [38] C. Vafa, private communication.
43. [39] N. Nekrasov, Holomorphic Bundles and Many-Body Systems, Comm. Math. Phys. 180 (1996) 587.
44. [40] E. Witten, Phase Transitions in M-Theory and F-Theory, Nucl. Phys. B 471 (1996) 195.
45. [41] A. Hanany and I.R. Klebanov, On Tensionless Strings in 3 + 1 Dimensions, hep-th/9606136.
46. [42] N. Seiberg, Nucl. Phys. B 435 (1995) 129.
47. [43] N. Nakayama, On Weierstrass models. Algebraic geometry and commutative algebra, Vol. II (Kinokuniya, Tokyo, 1988) p. 405-431.
48. [44] M. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. 7 (1957) 414.