Black holes and critical points in moduli space

Nuclear Physics B

Volumn 500, Issue 1-3, 1997, Pages 75-93

  Ferrara, Sergio ^a   Gibbons, Gary W ^b   Kallosh, Renata ^c  

^a CERN   (Switzerland)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031234460     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00324-6     Document Type: Article

References (47)

1. [1] G.W. Gibbons, Nucl. Phys. B 207 (1982) 337; P. Breitenlohner, D. Maison and G. Gibbons, Commun. Math. Phys. 120 (1988) 295.
2. [1] G.W. Gibbons, Nucl. Phys. B 207 (1982) 337; P. Breitenlohner, D. Maison and G. Gibbons, Commun. Math. Phys. 120 (1988) 295.
3. [2] G. Gibbons, R. Kallosh and B. Kol, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; D.A. Rasheed, hep-th/9702087.
4. [2] G. Gibbons, R. Kallosh and B. Kol, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; D.A. Rasheed, hep-th/9702087.
5. [3] S. Ferrara, R. Kallosh and A. Strominger, Phys. Rev. D 52 (1995) 5412, hep-th/9508072; A. Strominger, Phys. Lett. B 383 (1996) 39, hep-th/9602111.
6. [3] S. Ferrara, R. Kallosh and A. Strominger, Phys. Rev. D 52 (1995) 5412, hep-th/9508072; A. Strominger, Phys. Lett. B 383 (1996) 39, hep-th/9602111.
7. [4] S. Ferrara and R. Kallosh, Phys. Rev. D 54 (1996) 1514, hep-th 9602136; Phys. Rev. D 54 (1996) 1525, hep-th 9603090.
8. [4] S. Ferrara and R. Kallosh, Phys. Rev. D 54 (1996) 1514, hep-th 9602136; Phys. Rev. D 54 (1996) 1525, hep-th 9603090.
9. [5] R. Kallosh, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6284, hep-th/9607077; K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6293 hep-th/9608059; G.L. Cardoso, D. Lüst and T. Mohaupt, Phys. Lett. B 388 (1996) 266 hep-th/9608099.
10. [5] R. Kallosh, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6284, hep-th/9607077; K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6293 hep-th/9608059; G.L. Cardoso, D. Lüst and T. Mohaupt, Phys. Lett. B 388 (1996) 266 hep-th/9608099.
11. [5] R. Kallosh, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6284, hep-th/9607077; K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, Phys. Rev. D 54 (1996) 6293 hep-th/9608059; G.L. Cardoso, D. Lüst and T. Mohaupt, Phys. Lett. B 388 (1996) 266 hep-th/9608099.
12. [6] K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T, Mohaupt, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; Soo-Jong Rey, hep-th/9610157; M. Shmakova, hep-th/9612076.
13. [6] K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T, Mohaupt, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; Soo-Jong Rey, hep-th/9610157; M. Shmakova, hep-th/9612076.
14. [6] K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T, Mohaupt, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; Soo-Jong Rey, hep-th/9610157; M. Shmakova, hep-th/9612076.
15. [7] D. Kaplan, D. Lowe, J. Maldacena and A. Strominger, Phys. Rev. D 55 (1997) 4898, hep-th/9609204; K. Behrndt and T. Mohaupt, hep-th/9611140; J.M. Maldacena, hep-th/9611163.
16. [7] D. Kaplan, D. Lowe, J. Maldacena and A. Strominger, Phys. Rev. D 55 (1997) 4898, hep-th/9609204; K. Behrndt and T. Mohaupt, hep-th/9611140; J.M. Maldacena, hep-th/9611163.
17. [7] D. Kaplan, D. Lowe, J. Maldacena and A. Strominger, Phys. Rev. D 55 (1997) 4898, hep-th/9609204; K. Behrndt and T. Mohaupt, hep-th/9611140; J.M. Maldacena, hep-th/9611163.
18. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
19. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
20. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
21. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
22. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
23. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
24. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
25. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
26. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
27. [8] B. de Wit and A. van Proyen, Phys. Lett. B 293 (1992) 94; S. Ferrara and A. Strominger, in Strings '89, ed. R. Arnowitt, R. Bryan, M.J. Duff, D.V. Nanopoulos and C.N. Pope (World Scientific, Singapore, 1989) p. 245; A. Strominger, Commun. Math. Phys. 133 (1990) 163; L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 329 (1990) 27; P. Candelas and X.C. de la Ossa, Nucl. Phys. B 355 (1991) 455; L. Castellani, R. D' Auria and S. Ferrara, Phys. Lett. B 241 (1990) 57; Class. Quant. Grav. 7 (1990) 1767; R. D'Auria, S. Ferrara and P. Fré, Nucl. Phys. B 359 (1991) 705; B. de Wit and A. Van Proeyen, in Quaternionic Structures in Mathematics and Physics, ILAS/FM-6/1996 (Sissa, Trieste) hep-th/9505097; Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196.
28. [9] A. Ceresole, R. D'Auria, S. Ferrara and A. Van Proeyen, Nucl. Phys. B 444 (1995) 92, hep-th/9502072.
29. [10] A. Ceresole, R. D'Auria, S. Ferrara, Proceedings of the Trieste workshop on Mirror Symmetry and S-Duality, Trieste 1995, ed. K.S. Narain and E. Gava; hep-th 9509160.
30. [11] A. Strominger, Nucl. Phys. B 451 (1995) 96, hep-th/9504090
31. [12] K. Behrndt, Nucl. Phys. B 455 (1995) 188, hep-th/9506106; M. Cvetič and D. Youm, Phys. Lett. B 359 (1995) 87, hep-th/9507160; K.L. Chan and M. Cvetič, Phys. Lett. B 375 (1996) 98, hep-th/9512188; G.W. Gibbons and D.A. Rasheed, Nucl. Phys. B 476 (1996) 515, hep-th/9604177; T. Ortin, Phys. Rev. Lett. 76 (1996) 3890, hep-th/9602067.
32. [12] K. Behrndt, Nucl. Phys. B 455 (1995) 188, hep-th/9506106; M. Cvetič and D. Youm, Phys. Lett. B 359 (1995) 87, hep-th/9507160; K.L. Chan and M. Cvetič, Phys. Lett. B 375 (1996) 98, hep-th/9512188; G.W. Gibbons and D.A. Rasheed, Nucl. Phys. B 476 (1996) 515, hep-th/9604177; T. Ortin, Phys. Rev. Lett. 76 (1996) 3890, hep-th/9602067.
33. [12] K. Behrndt, Nucl. Phys. B 455 (1995) 188, hep-th/9506106; M. Cvetič and D. Youm, Phys. Lett. B 359 (1995) 87, hep-th/9507160; K.L. Chan and M. Cvetič, Phys. Lett. B 375 (1996) 98, hep-th/9512188; G.W. Gibbons and D.A. Rasheed, Nucl. Phys. B 476 (1996) 515, hep-th/9604177; T. Ortin, Phys. Rev. Lett. 76 (1996) 3890, hep-th/9602067.
34. [12] K. Behrndt, Nucl. Phys. B 455 (1995) 188, hep-th/9506106; M. Cvetič and D. Youm, Phys. Lett. B 359 (1995) 87, hep-th/9507160; K.L. Chan and M. Cvetič, Phys. Lett. B 375 (1996) 98, hep-th/9512188; G.W. Gibbons and D.A. Rasheed, Nucl. Phys. B 476 (1996) 515, hep-th/9604177; T. Ortin, Phys. Rev. Lett. 76 (1996) 3890, hep-th/9602067.
35. [12] K. Behrndt, Nucl. Phys. B 455 (1995) 188, hep-th/9506106; M. Cvetič and D. Youm, Phys. Lett. B 359 (1995) 87, hep-th/9507160; K.L. Chan and M. Cvetič, Phys. Lett. B 375 (1996) 98, hep-th/9512188; G.W. Gibbons and D.A. Rasheed, Nucl. Phys. B 476 (1996) 515, hep-th/9604177; T. Ortin, Phys. Rev. Lett. 76 (1996) 3890, hep-th/9602067.
36. [13] R. Kallosh and A. Linde, Phys. Rev. D 52 (1995) 7137, hep-th/9507022.
37. [14] K. Behrndt, Phys. Lett. B 396 (1997) 77, hep-th/9610232.
38. [15] L. Andrianopoli, R. D'Auria and S. Ferrara, hep-th/9612105.
39. [16] G. Ruppeiner, Rev. Mod. Phys. 67 605 (1995); 68 (1996) 313 (E).
40. [16] G. Ruppeiner, Rev. Mod. Phys. 67 605 (1995); 68 (1996) 313 (E).
41. [17] P. Fré, hep-th/9701054.
42. [18] A. Chou, R. Kallosh, J. Rahmfeld, S-J. Rey, M. Shmakova and W.K. Wong, hep-th/9704142.
43. [19] G.W. Gibbons and K. Maeda, Nucl. Phys. B 298 (1988) 741.
44. [20] J. Preskill, P. Schwarz, A. Shapere, S. Trivedi and F. Wilczek, Mod. Phys. Lett. A 6 (1991) 2353.
45. [21] R. Kallosh, A. Linde, T. Ortín, A. Peet and A. Van Proeyen, Phys. Rev. D 46 (1992) 5278.
46. [22] R. Kallosh, Phys. Rev. D 55 (1997) 3241, hep-th/9611162.
47. [23] E. Witten, Nucl. Phys. B 471 (1996) 195, hep-th/9603150.