Attractors at weak gravity

Nuclear Physics B

Volumn 547, Issue 1-2, 1999, Pages 201-220

  Denef, Frederik ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

(Quantum and gravity corrected) monopoles; 4D, N = 2 string theory compactifications; Attractor mechanism; Supergravity solutions; Supersymmetric Yang Mills theory

Indexed keywords

EID: 0033541902     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00096-6     Document Type: Article

References (62)

1. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
2. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
3. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
4. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
5. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
6. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
7. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; S. Katz, A. Klemm and C. Vafa, Geometrical engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173, hep-th/9609239; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories I, Adv. Theor. Math. Phys. 1 (1998) 53, hep-th/9706110; A. Klemm, On the Geometry behind N = 2 Supersymmetric Effective Actions in Four Dimensions, hep-th/9705131; W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) 55B (1997) 83; Fortsch. Phys. 45 (1997) 293, hep-th/9611190.
8. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
9. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
10. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
11. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
12. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
13. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 ( 1997) 3, hep-th/9703166; M. Douglas and M. Li, D-brane Realization of script N = 2 Super Yang-Mills Theory in Four Dimensions, hep-th/9604041; P. Howe, N. Lambert and P. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th/9710034; N. Lambert and P. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; Brane Dynamics and Four-dimensional Quantum Field Theory, hep-th/9811177.
14. J. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231, hep-th/9711200; S. Gubser, I. Klebanov and A. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105, hep-th/9802109; E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253, hep-th/9802150.
15. J. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231, hep-th/9711200; S. Gubser, I. Klebanov and A. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105, hep-th/9802109; E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253, hep-th/9802150.
16. J. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231, hep-th/9711200; S. Gubser, I. Klebanov and A. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105, hep-th/9802109; E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253, hep-th/9802150.
17. S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412, hep-th/9508072.
18. S. Ferrara, G. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75, hep-th/9702103.
19. G. Moore, Arithmetic and Attractors, hep-th/9807087.
20. G. Moore, Attractors and Arithmetic, hep-th/9807056.
21. M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, The rigid limit in special Kahler geometry, Class. Quant. Grav. 15 (1998) 2083, hep-th/9803228; M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, Special Geometry of Calabi-Yau Compactifications Near a Rigid Limit, hep-th/9801140; S. Cacciatori and D. Zanon, Gravitational Corrections to N = 2 Supersymmetric Lagrangians, hep-th/9809202.
22. M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, The rigid limit in special Kahler geometry, Class. Quant. Grav. 15 (1998) 2083, hep-th/9803228; M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, Special Geometry of Calabi-Yau Compactifications Near a Rigid Limit, hep-th/9801140; S. Cacciatori and D. Zanon, Gravitational Corrections to N = 2 Supersymmetric Lagrangians, hep-th/9809202.
23. M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, The rigid limit in special Kahler geometry, Class. Quant. Grav. 15 (1998) 2083, hep-th/9803228; M. Billó, F. Denef, P. Frè, I. Pesando, W. Troost, A. Van Proeyen and D. Zanon, Special Geometry of Calabi-Yau Compactifications Near a Rigid Limit, hep-th/9801140; S. Cacciatori and D. Zanon, Gravitational Corrections to N = 2 Supersymmetric Lagrangians, hep-th/9809202.
24. T. Banks, M. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 278 hep-th/9605199.
25. A. Sen, BPS states on a three brane probe, Phys. Rev. D 55 (1997) 2501, hep-th/9608005.
26. M.R. Gaberdiel, T. Hauer and B. Zwiebach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117, hep-th/9801205; O. Bergman and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys. B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories Nucl. Phys. B 531 (1998) 345, hep-th/9803142; O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Constraints on the BPS spectrum of N = 2, D = 4 theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220.
27. M.R. Gaberdiel, T. Hauer and B. Zwiebach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117, hep-th/9801205; O. Bergman and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys. B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories Nucl. Phys. B 531 (1998) 345, hep-th/9803142; O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Constraints on the BPS spectrum of N = 2, D = 4 theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220.
28. M.R. Gaberdiel, T. Hauer and B. Zwiebach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117, hep-th/9801205; O. Bergman and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys. B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories Nucl. Phys. B 531 (1998) 345, hep-th/9803142; O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Constraints on the BPS spectrum of N = 2, D = 4 theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220.
29. M.R. Gaberdiel, T. Hauer and B. Zwiebach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117, hep-th/9801205; O. Bergman and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys. B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories Nucl. Phys. B 531 (1998) 345, hep-th/9803142; O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Constraints on the BPS spectrum of N = 2, D = 4 theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220.
30. J. Barrow, Varying G and Other Constants, gr-qc/9711084; J. Webb, V. Flambaum, C. Curchill, M. Drinkwater and J. Barrow, Evidence for Time Variation of the Fine Structure Constant, astro-ph/9803165.
31. J. Barrow, Varying G and Other Constants, gr-qc/9711084; J. Webb, V. Flambaum, C. Curchill, M. Drinkwater and J. Barrow, Evidence for Time Variation of the Fine Structure Constant, astro-ph/9803165.
32. M. Volkov and D. Gal'tsov, Gravitating Non-abelian Solitons and Black Holes with Yang-mills Fields, hep-th/9810070.
33. G. Chalmers, M. Rocek and R. von Unge, Monopoles in Quantum Corrected N = 2 Super Yang-Mills Theory, hep-th/9612195.
34. J. Gauntlett, Jq. Gomis and P. Townsend, BPS bounds for world volume branes, J. High Energy Phys. (1998) 01:003, hep-th/9711205.
35. N. Lambert and P. West, Monopole Dynamics from the M-fivebrane, hep-th/9811025.
36. C. Callan and J. Maldacena, Brane dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198; A. Hashimoto, The shape of branes pulled by strings, Phys. Rev. D 57 (1998) 6441, hep-th/9711097.
37. C. Callan and J. Maldacena, Brane dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198; A. Hashimoto, The shape of branes pulled by strings, Phys. Rev. D 57 (1998) 6441, hep-th/9711097.
38. B. de Wit, P. Lauwers and A. Van Proeyen Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569; B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special geometry?, Nucl. Phys. B 503 (1997) 565, hep-th/9703082.
39. B. de Wit, P. Lauwers and A. Van Proeyen Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569; B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special geometry?, Nucl. Phys. B 503 (1997) 565, hep-th/9703082.
40. I. Gaida, H. Hollmann and J. Stewart, Classical and Quantum Analysis of Repulsive Singularities in Four-dimensional Extended Supergravity, hep-th/9811032.
41. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B383 (1996) 39, hep-th/9602111; S. Ferrara, R. Kallosh Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; R. Kallosh and A. Linde, Black hole superpartners and fixed scalars, Phys. Rev. D 56 (1997) 3509, hep-th/9611161; P. Fré, Supersymmetry and first-order equations for extremal states: Monoploes, hyperinstantons, blackholes and p-branes, Nucl. Phys. B (Proc. Suppl.) 57 (1997) 52, hep-th/9701054.
42. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B383 (1996) 39, hep-th/9602111; S. Ferrara, R. Kallosh Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; R. Kallosh and A. Linde, Black hole superpartners and fixed scalars, Phys. Rev. D 56 (1997) 3509, hep-th/9611161; P. Fré, Supersymmetry and first-order equations for extremal states: Monoploes, hyperinstantons, blackholes and p-branes, Nucl. Phys. B (Proc. Suppl.) 57 (1997) 52, hep-th/9701054.
43. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B383 (1996) 39, hep-th/9602111; S. Ferrara, R. Kallosh Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; R. Kallosh and A. Linde, Black hole superpartners and fixed scalars, Phys. Rev. D 56 (1997) 3509, hep-th/9611161; P. Fré, Supersymmetry and first-order equations for extremal states: Monoploes, hyperinstantons, blackholes and p-branes, Nucl. Phys. B (Proc. Suppl.) 57 (1997) 52, hep-th/9701054.
44. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B383 (1996) 39, hep-th/9602111; S. Ferrara, R. Kallosh Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; R. Kallosh and A. Linde, Black hole superpartners and fixed scalars, Phys. Rev. D 56 (1997) 3509, hep-th/9611161; P. Fré, Supersymmetry and first-order equations for extremal states: Monoploes, hyperinstantons, blackholes and p-branes, Nucl. Phys. B (Proc. Suppl.) 57 (1997) 52, hep-th/9701054.
45. A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B383 (1996) 39, hep-th/9602111; S. Ferrara, R. Kallosh Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992, hep-th/9607108; R. Kallosh and A. Linde, Black hole superpartners and fixed scalars, Phys. Rev. D 56 (1997) 3509, hep-th/9611161; P. Fré, Supersymmetry and first-order equations for extremal states: Monoploes, hyperinstantons, blackholes and p-branes, Nucl. Phys. B (Proc. Suppl.) 57 (1997) 52, hep-th/9701054.
46. S.J. Rey, Classical and quantum aspects of BPS black holes in N = 2, D = 4 heterotic string compactifications; Nucl. Phys. B 508 (1997) 569, hep-th/9610157.
47. K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540, hep-th/9612076; W. Sabra, General static N = 2 black holes, Mod. Phys. Lett. A 12 (1997) 2585, hep-th/9703101; Black holes in N = 2 supergravity theories and harmonic functions, Nucl. Phys. B 510 (1998) 247, hep-th/9704147; K. Behrndt, D. Lüst and W. Sabra, Stationary solutions of N = 2 supergravity Nucl. Phys. B 510 (1998) 264, hep-th/9705169.
48. K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540, hep-th/9612076; W. Sabra, General static N = 2 black holes, Mod. Phys. Lett. A 12 (1997) 2585, hep-th/9703101; Black holes in N = 2 supergravity theories and harmonic functions, Nucl. Phys. B 510 (1998) 247, hep-th/9704147; K. Behrndt, D. Lüst and W. Sabra, Stationary solutions of N = 2 supergravity Nucl. Phys. B 510 (1998) 264, hep-th/9705169.
49. K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540, hep-th/9612076; W. Sabra, General static N = 2 black holes, Mod. Phys. Lett. A 12 (1997) 2585, hep-th/9703101; Black holes in N = 2 supergravity theories and harmonic functions, Nucl. Phys. B 510 (1998) 247, hep-th/9704147; K. Behrndt, D. Lüst and W. Sabra, Stationary solutions of N = 2 supergravity Nucl. Phys. B 510 (1998) 264, hep-th/9705169.
50. K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540, hep-th/9612076; W. Sabra, General static N = 2 black holes, Mod. Phys. Lett. A 12 (1997) 2585, hep-th/9703101; Black holes in N = 2 supergravity theories and harmonic functions, Nucl. Phys. B 510 (1998) 247, hep-th/9704147; K. Behrndt, D. Lüst and W. Sabra, Stationary solutions of N = 2 supergravity Nucl. Phys. B 510 (1998) 264, hep-th/9705169.
51. K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236, hep-th/9610105; M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540, hep-th/9612076; W. Sabra, General static N = 2 black holes, Mod. Phys. Lett. A 12 (1997) 2585, hep-th/9703101; Black holes in N = 2 supergravity theories and harmonic functions, Nucl. Phys. B 510 (1998) 247, hep-th/9704147; K. Behrndt, D. Lüst and W. Sabra, Stationary solutions of N = 2 supergravity Nucl. Phys. B 510 (1998) 264, hep-th/9705169.
52. K. Behrndt, D. Lüst and W. Sabra, Moving moduli, Calabi-Yau phase transitions and massless BPS configurations in type II superstrings, Phys. Lett. B 418 (1998) 303, hep-th/9708065.
53. A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995) 96, hep-th/9504090.
54. G.'t Hooft, The scattering matrix approach for the quantum black hole: An overview, Int. J. Mod. Phys. A 11 ( 1996) 4623, gr-qc/9607022; P. Aichelburg and R. Sexl, Gen. Rel. Grav. 2 (1971) 303; W. Bonner, Commun. Math. Phys. 13 (1969) 163.
55. G.'t Hooft, The scattering matrix approach for the quantum black hole: An overview, Int. J. Mod. Phys. A 11 ( 1996) 4623, gr-qc/9607022; P. Aichelburg and R. Sexl, Gen. Rel. Grav. 2 (1971) 303; W. Bonner, Commun. Math. Phys. 13 (1969) 163.
56. G.'t Hooft, The scattering matrix approach for the quantum black hole: An overview, Int. J. Mod. Phys. A 11 ( 1996) 4623, gr-qc/9607022; P. Aichelburg and R. Sexl, Gen. Rel. Grav. 2 (1971) 303; W. Bonner, Commun. Math. Phys. 13 (1969) 163.
57. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087.
58. O. Bergman, Stable Non-BPS Dyons in N = 2 SYM, hep-th/9811064; A. Sen, D-branes on Non-supersymmetric Cycles, hep-th/9812031.
59. O. Bergman, Stable Non-BPS Dyons in N = 2 SYM, hep-th/9811064; A. Sen, D-branes on Non-supersymmetric Cycles, hep-th/9812031.
60. R. Koch and R. Tatar, Higher Derivative Terms from Threebranes in F Theory, hep-th/9811128.
61. K. Hashimoto, H. Hata and N. Sasakura, Multi-pronged Strings and BPS Saturated Solutions in SU(n) Supersymmetric Yang-Mills Theory, hep-th/9804164;
62. K. Lee and P. Li, Dyons in N = 4 Supersymmetric Theories and Three-pronged Strings, hep-th/9804174.