E-strings and N = 4 topological Yang-Mills theories

Nuclear Physics B

Volumn 527, Issue 3, 1998, Pages 581-623

  Minahan, J A ^a   Nemeschansky, D ^a   Vafa, C ^b   Warner, N P ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032494034     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00426-X     Document Type: Article

References (55)

1. [1] A. Strominger and C. Vafa, Phys. Lett. B 379 (1996) 99, hep-th/9601029.
2. [2] J. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, hep-th/9711053.
3. [3] C. Vafa, Black holes and Calabi-Yau three-folds, HUTP-97-A066, hep-th/9711067.
4. [4] E. Witten, Some comments on string dynamics, IASSNS-HEP-95-63, hep-th/9507121; in Strings '95: Future Perspectives in String Theory, ed. I. Bars, P. Bouwknegt, J. Minahan, D. Nemeschansky, K. Pilch, H. Saleur and N.P. Warner, Proceedings of USC conference, Los Angeles, March 13-18, 1995 (World Scientific, Singapore, 1996).
5. [5] O. Ganor and A. Hanany, Nucl. Phys. B 474 (1996) 122, hep-th/9602120.
6. [6] N. Seiberg and E. Witten, Nucl. Phys. B 471 (1996) 121, hep-th/9603003.
7. [7] D. Morrison and C. Vafa, Compactifications of F-Theory on Calabi-Yau Threefolds I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Compactifications of F-Theory on Calabi-Yau Threefolds II, Nucl. Phys. B 476 (1996) 437, hep-th/9603161.
8. [7] D. Morrison and C. Vafa, Compactifications of F-Theory on Calabi-Yau Threefolds I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Compactifications of F-Theory on Calabi-Yau Threefolds II, Nucl. Phys. B 476 (1996) 437, hep-th/9603161.
9. [8] E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195, hep-th/9603150.
10. [9] A. Klemm, P. Mayr and C. Vafa, BPS states of exceptional non-critical strings, to appear in Proc. Conf. Advanced Quantum Field Theory (in memory of Claude Itzykson), CERN-TH-96-184, hep-th/9607139.
11. n strings, Nucl. Phys. B 508 (1997) 64; hep-th/9705237.
12. 8 non-critical string, USC-97/009, NSF-ITP-97-091, hep-th/9707149.
13. [12] C. Vafa and E. Witten, A strong coupling test of S-duality Nucl. Phys. B 431 (1994) 3, hep-th/9408074.
14. [13] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Nucl. Phys. B 405 (1993) 279, hep-th/9302103; Comm. Math. Phys. 165 (1994) 311, hep-th/9309140.
15. [13] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Nucl. Phys. B 405 (1993) 279, hep-th/9302103; Comm. Math. Phys. 165 (1994) 311, hep-th/9309140.
16. [14] C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403, hep-th/9602022.
17. [15] H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl. Phys. B 463 (1996) 55, hep-th/95111164.
18. [16] A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44, hep-th/9512059.
19. [17] M. Bershadsky, V. Sadov and C. Vafa, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420, hep-th/9511222.
20. [18] M. Douglas, Branes within branes, hep-th/9512077.
21. [19] C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435, hep-th/9512078.
22. [20] R Friedman, J.W. Morgan and E. Witten, Vector bundles over elliptic fibrations, alg-geom/9709029.
23. [21] M. Bershadsky, A. Johansen, T. Pantev and V. Sadov, On four-dimensional compactifications of F-theory, Nucl. Phys. B 505 (1997) 165; hep-th/9701165.
24. [22] W. Lerche, P. Mayr and N.P. Warner, Non-critical strings, del Pezzo singularities and Seiberg-Witten curves, Nucl. Phys. B 499 (1997) 125; hep-th/9612085.
25. [23] S. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239.
26. [24] E. Witten, Physical interpretation of certain strong coupling singularities, Mod. Phys. Let. A 11 (1996) 2649, hep-th/9609159.
27. [25] M. Bershadsky and C. Vafa, Global anomalies and geometric engineering of critical theories in six dimensions, hep-th/9703167.
28. [26] E. Verlinde, Global aspects of electric-magnetic duality, Nucl. Phys. B 455 (1995) 211; hep-th/9506011.
29. [27] O.J. Ganor, Compactification of tensionless string theories, hep-th/9607092.
30. [28] G. 't Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1; A property of electric and magnetic flux in non-abelian gauge theories, Nucl. Phys. B 153 (1979) 141.
31. [28] G. 't Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1; A property of electric and magnetic flux in non-abelian gauge theories, Nucl. Phys. B 153 (1979) 141.
32. [29] R. Dijkgraaf, E. Verlinde and H. Verlinde, Nucl. Phys. B 486 (1997) 89.
33. [30] R. Dijkgraaf, G. Moore, E. Verlinde and H. Verlinde, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 (1997) 197, hep-th/9608096.
34. [31] S. Lang, Introduction to Modular Forms (Springer, Berlin, 1976).
35. [32] G. Moore and E. Witten, Integration over the u-plane in Donaldson theory, hep-th/9709193.
36. [33] A. Lossev, N. Nekrassov and S. Shatashvili, Testing Seiberg-Witten solution, hep-th/9801061.
37. [34] C. Itzykson, Int. J. Mod. Phys. A B 8 (1994) 1994.
38. [35] T. Pantev, private communication.
39. [36] S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, hep-th/9706110.
40. [37] N.C. Leung and C. Vafa, Branes and toric geometry, hep-th/9711013.
41. [38] C. Vafa and E. Witten, On orbifolds with discrete torsion, J. Geom. Phys. 15 (1995) 189, hep-th/9409188.
42. [39] J. Minahan, D. Nemeschansky and N.P. Warner, Instanton expansions for mass deformed N = 4 super Yang-Mills theories, USC-97/016, hep-th/9710146.
43. [40] O. Ganor, D. Morrison and N. Seiberg, Nucl. Phys. B 487 (1997) 93, hep-th/9610251.
44. [41] S.-T. Yau, Essays on Mirror Manifolds (International Press, Hong Kong, 1992).
45. [42] N. Seiberg; and E. Witten, Nucl. Phys. B 426(1994) 19, hep-th/9407087; Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
46. [42] N. Seiberg; and E. Witten, Nucl. Phys. B 426(1994) 19, hep-th/9407087; Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
47. [43] O.J. Ganor, A test of the chiral E8 current algebra on a 6D non-critical string, Nucl. Phys. B 479 (1996) 197; hep-th/9607020.
48. [44] S. Cecotti, P. Fendley, K. Intriligator and C. Vafa, A new supersymmetric index, Nucl. Phys. B 385 (1992) 405, hep-th/9204102.
49. [45] M.R. Douglas, S. Katz and C. Vafa, Nucl. Phys. B 497 (1997) 155, hep-th/9609071.
50. [46] D.R. Morrison and N. Seiberg, Nucl. Phys. B 483 (1997) 229, hep-th/9609070.
51. 2, preprint, Kyoto University; The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface, preprint, Kyoto University; A.A. Klyachko, Moduli of vector bundles and numbers of classes, Funct. Anal. Appl. 25 (1991) 67.
52. 2, preprint, Kyoto University; The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface, preprint, Kyoto University; A.A. Klyachko, Moduli of vector bundles and numbers of classes, Funct. Anal. Appl. 25 (1991) 67.
53. 2, preprint, Kyoto University; The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface, preprint, Kyoto University; A.A. Klyachko, Moduli of vector bundles and numbers of classes, Funct. Anal. Appl. 25 (1991) 67.
54. [48] K. Yoshioka, to appear.
55. + = 1, alg-geom/9612020.