Colliding singularities in F-theory and phase transitions

Nuclear Physics B

Volumn 489, Issue 1-2, 1997, Pages 122-138

  Bershadsky, Michael ^a   Johansen, Andrei ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Colliding singularities; F theory; Tensionless strings

Indexed keywords

EID: 0031592530     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00027-8     Document Type: Article

References (27)

1. [1] C. Vafa, Nucl. Phys. B 469 (1996) 403, hep-th/9602022.
2. [2] D. Morrison and C. Vafa, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Nucl. Phys. B 476 (1996) 437, hep-th/9603161.
3. [2] D. Morrison and C. Vafa, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; Nucl. Phys. B 476 (1996) 437, hep-th/9603161.
4. [3] M. Bershadsky, K. Intriligator, S. Kachru, D. Morrison, V. Sadov and C. Vafa, Nucl. Phys. B 481 (1996) 215, hep-th/9605200.
5. [4] S. Katz and C. Vafa, Matter From Geometry, hep-th/9606086.
6. [5] T. Banks, M.R. Douglas and N. Seiberg, Phys. Lett. B 387 (1996) 278, hep-th/9605199; N. Seiberg, Phys. Lett. B 384 (1996) 81, hep-th/9606017.
7. [5] T. Banks, M.R. Douglas and N. Seiberg, Phys. Lett. B 387 (1996) 278, hep-th/9605199; N. Seiberg, Phys. Lett. B 384 (1996) 81, hep-th/9606017.
8. [6] E. Wirten, Nucl. Phys. B 460 (1996) 335.
9. [7] A. Sen, Nucl. Phys. B 475 (1996) 562, hep-th/9605150.
10. [8] K. Dasgupta and S. Mukhi, Phys. Lett. B 385 (1996) 125, hep-th/9606044.
11. [9] A. Johansen, A Comment on BPS States in F-theory in 8 Dimensions, HUTP-96/A030, hep-th/9608186.
12. [10] P. Aspinwall and M. Gross, Phys. Lett. B 387 (1996) 735, hep-th/9605131.
13. [11] N. Seiberg and E. Witten, Nucl. Phys. B 471 (1996) 121, hep-th/9603003.
14. [12] M.R. Douglas, S. Katz and C. Vafa, Small Instantons, Del Pezzo Surfaces and type I Theory, hep-th/9609071.
15. [13] A. Klemm, P. Mayr and C. Vafa, BPS States of Exceptional Non-critical Strings, hep-th/9607139.
16. [14] E. Witten, Physical Interpretation of Certain Strong Coupling Singularities, IASSNS-HEP-96/97, hep-th/9609159.
17. [15] N. Seiberg, Non-trivial Fixed Points of the Renormalization Group in Six Dimensions, RU-96-85, hep-th/9609161.
18. [16] M.B. Green and J.H. Schwarz, Phys. Lett. B 149 (1984) 117.
19. [17] A. Sagnotti, Phys. Lett. B 294 (1992) 196, hep-th/9210127.
20. [18] V. Sadov, Phys. Lett. B 388 (1996) 45, hep-th/9606008.
21. [19] M. Bershadsky, V. Sadov and C. Vafa, Nucl. Phys. B 463 (1996) 398.
22. [20] R-Hartshorne, Algebraic Geometry (Springer, Berlin).
23. [21] R. Miranda, Smooth Models for Elliptic Threefolds, in The Birational Geometry of Degenerations, ed. R. Friedman and D.R. Morrison (Birkhäuser, Basel, 1983).
24. [22] J.D. Blum and A. Zaffaroni, Phys. Lett. B 387 (1996) 71, hep-th/9607019; J.D. Blum, F Theory Orientifolds, M Theory Orientifolds, and Twisted Strings, hep-th/9608053.
25. [22] J.D. Blum and A. Zaffaroni, Phys. Lett. B 387 (1996) 71, hep-th/9607019; J.D. Blum, F Theory Orientifolds, M Theory Orientifolds, and Twisted Strings, hep-th/9608053.
26. [23] S. Ferrara, R. Minasian and A. Sagnotti, Nucl. Phys. B 474 (1996) 323, hep-th/9604097; C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y.S. Stanev, Phys. Lett. B 387 (1996) 743, hep-th/9607229.
27. [23] S. Ferrara, R. Minasian and A. Sagnotti, Nucl. Phys. B 474 (1996) 323, hep-th/9604097; C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y.S. Stanev, Phys. Lett. B 387 (1996) 743, hep-th/9607229.