Short-distance space-time structure and black holes in string theory: A short review of the present status

Chaos, solitons and fractals

Volumn 10, Issue 2, 1999, Pages 423-443

  Li, Miao ^a   Yoneya, Tamiaki ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

HOLOGRAPHY; MATHEMATICAL MODELS;

BLACK HOLE PHYSICS; SHORT-DISTANCE SPACE-TIME STRUCTURES; STRING THEORY;

QUANTUM THEORY;

EID: 0033077388     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00198-2     Document Type: Article

References (82)

1. G. Veneziano, Nuovo Cim. 57A(1968) 190.
2. We want to emphasize that the bibliography of the present paper is not, in any sense, aiming a complete listing of all relevant works. We would like to apologize all authors if their works related to our subjects are not cited here. For more extensive reviews and references on general string theory, we refer the reader to M. Green, J. Schwarz and E. Witten, Superstring Theory, Vols 1 and 2. Cambridge Univ. Press (1987), J. Schwarz (ed.), Superstrings: the First 15 Years of Superstring Theory, Vol 1 and 2, World Scientific (1985), and other review articles referred to below.
3. We want to emphasize that the bibliography of the present paper is not, in any sense, aiming a complete listing of all relevant works. We would like to apologize all authors if their works related to our subjects are not cited here. For more extensive reviews and references on general string theory, we refer the reader to M. Green, J. Schwarz and E. Witten, Superstring Theory, Vols 1 and 2. Cambridge Univ. Press (1987), J. Schwarz (ed.), Superstrings: the First 15 Years of Superstring Theory, Vol 1 and 2, World Scientific (1985), and other review articles referred to below.
4. Y. Nambu, Proc. Intl. Conf. on Symmetries and Quark Models (Wayne State Univ.)(1969). H. B. Nielsen, 15th Conf. on High Energy Physics (Kiev)(1970). L. Susskind, Nuovo Cim. 69 (1970) 457.
5. Y. Nambu, Proc. Intl. Conf. on Symmetries and Quark Models (Wayne State Univ.)(1969). H. B. Nielsen, 15th Conf. on High Energy Physics (Kiev)(1970). L. Susskind, Nuovo Cim. 69 (1970) 457.
6. Y. Nambu, Proc. Intl. Conf. on Symmetries and Quark Models (Wayne State Univ.)(1969). H. B. Nielsen, 15th Conf. on High Energy Physics (Kiev)(1970). L. Susskind, Nuovo Cim. 69 (1970) 457.
7. J. A. Shapiro, Phys. Rev. D11(1975) 2937.
8. T. Yoneya, Prog. Theor. Phys. 51(1974) 1907; Lett. Nuovo. Cim. 8(1973)951; Prog. Theor. Phys. 56(1976)1310.
9. T. Yoneya, Prog. Theor. Phys. 51(1974) 1907; Lett. Nuovo. Cim. 8(1973)951; Prog. Theor. Phys. 56(1976)1310.
10. T. Yoneya, Prog. Theor. Phys. 51(1974) 1907; Lett. Nuovo. Cim. 8(1973)951; Prog. Theor. Phys. 56(1976)1310.
11. J. Scherk and J. Schwarz, Nucl. Phys. B81(1974)118; Phys. Lett. 57B(1975)463.
12. J. Scherk and J. Schwarz, Nucl. Phys. B81(1974)118; Phys. Lett. 57B(1975)463.
13. F. Gliozzi, J. Scherk and D. Olive, Nucl. Phys. B122 (1977)253.
14. For a review on recent developments, see, e.g., J. Polchinski, Rev. Mod. Phys. 68(1996)1245.
15. K. Kikkawa and M. Yamasaki, Phys. Lett. B149(1984)357.
16. A. Sen, Int. Jour. Mod. Phys. A9(1994)3707.
17. E. Witten, Nucl. Phys. B443(1995)85.
18. J. Polchinski, Phys. Rev. Lett. 75(1995)4724.
19. G. Horowitz and A. Strominger, Nucl. Phys. B360 (1991)197.
20. A. Strominger and C. Vafa, Phys. Lett. B379(1996)99.
21. For reviews, see, e.g., J. Maldacena, hep-th/9607235; A. W. Peet, hep-th/9712253.
22. E. Witten, Nucl. Phys. B460(1996)335.
23. T. Banks, W. Fischler, S. H. Shenker and L. Susskind, Phys. Rev. D55(1997)5112.
24. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, Nucl. Phys B498(1997)467.
25. L. Susskind, hep-th/9704080.
26. N. Seiberg, Phys. Rev. Lett. 79(1997) 3577. See also, A. Sen, hep-th/9709220.
27. For a previous review on space-time uncertainty principle, see T. Yoneya, hep-th/9707002 (to appear in the Proceedings of the APCPT-ICTP Joint International Conference '97).
28. T. Yoneya, Duality and Indeterminacy Principle in String Theory, in "Wandering in the Fields", eds. K. Kawarabayashi and A. Ukawa (World Scientific, 1987), p. 419: see also String Theory and Quantum Gravity in "Quantum String Theory", eds. N. Kawamoto and T. Kugo (Springer, 1988), p. 23.
29. T. Yoneya, Duality and Indeterminacy Principle in String Theory, in "Wandering in the Fields", eds. K. Kawarabayashi and A. Ukawa (World Scientific, 1987), p. 419: see also String Theory and Quantum Gravity in "Quantum String Theory", eds. N. Kawamoto and T. Kugo (Springer, 1988), p. 23.
30. D. Amati, M. Ciafaloni and G. Veneziano, Phys. Lett. 197B, 81(1987).
31. D. Gross and P. Mende, Nucl. Phys. B303, 407(1988).
32. For a review and a list of references related to this subject, see, e. g., L. J. Garay, Int. J. Mod. Phys. A10, 145(1995). For other recent attemps, see also G. Amelio-Camelin, J. Ellis, N. E. Mavromatos and D. V. Nanopoulos, hep-th/9701144 and references therein.
33. T. Yoneya, Mod. Phys. Lett. A4, 1587(1989).
34. M. Li and T. Yoneya, Phys. Rev. Lett. 78 (1997) 1219.
35. J. J. Atick and E. Witten, Nucl. Phys. B310, 291(1988).
36. See, e.g., S. Doplicher, K. Fredenhagen and J. E. Roberts, Commun. Math. Phys. 172 (1995) 187; Phys. Lett. B331 (1994) 39, and references therein.
37. See, e.g., S. Doplicher, K. Fredenhagen and J. E. Roberts, Commun. Math. Phys. 172 (1995) 187; Phys. Lett. B331 (1994) 39, and references therein.
38. A. Jevicki, M. Li and T. Yoneya, Nucl. Phys. B448(1995) 277.
39. I. Klebanov, Proceedings of the Trieste Spring School 1991, eds. J. Harvey et al. (World Scientific, Singapore, 1991); A. Jevicki, hep-th/9309115; J. Polchinski, hep-th/9411028.
40. S. Shenker, hep-th/9509132.
41. L. Susskind, Phys. Rev. D49 (1994) 6606.
42. A. Jevicki and T. Yoneya, Nucl. Phys. B411(1994) 64.
43. T. Yoneya, p. 178, in "Frontiers in Quantum Field Theories" (World Scientific, 1996), hep-th/9603096.
44. For review, see, e.g., L. Susskind, hep-th/9511227; D. Bigatti and L. Susskind, hep-th/9712072.
45. T. Yoneya, Proc. of the Sixth Workshop on General Relativity and Gravitation (Dec. 2-5, 1996).
46. M. Douglas, D. Kabat, P. Pouliot and S. Shenker, Nucl. Phys. B485(1997)85.
47. G. Horowitz and J. Polchinski, Phys. Rev. D55(1977)6189.
48. G. 'tHooft, Dimensional Reduction in Quantum Gravity, gr-qc/9310026; L. Susskind, J. Math. Phys. 36(1995)6377.
49. G. 'tHooft, Dimensional Reduction in Quantum Gravity, gr-qc/9310026; L. Susskind, J. Math. Phys. 36(1995)6377.
50. T. Yoneya, Phys. Lett. 197B(1987) 76; R. C. Myers, S. Penati, M. Pernici, and A. Strominger, Nucl. Phys. B310(1988)25; H. Hata and Y. Nagoshi, Prog. Theor. Phys. 80(1988) 80; O. Bergman and B. Zwiebach, Nucl. Phys. B441 (1995) 441.
51. T. Yoneya, Phys. Lett. 197B(1987) 76; R. C. Myers, S. Penati, M. Pernici, and A. Strominger, Nucl. Phys. B310(1988)25; H. Hata and Y. Nagoshi, Prog. Theor. Phys. 80(1988) 80; O. Bergman and B. Zwiebach, Nucl. Phys. B441 (1995) 441.
52. T. Yoneya, Phys. Lett. 197B(1987) 76; R. C. Myers, S. Penati, M. Pernici, and A. Strominger, Nucl. Phys. B310(1988)25; H. Hata and Y. Nagoshi, Prog. Theor. Phys. 80(1988) 80; O. Bergman and B. Zwiebach, Nucl. Phys. B441 (1995) 441.
53. T. Yoneya, Phys. Lett. 197B(1987) 76; R. C. Myers, S. Penati, M. Pernici, and A. Strominger, Nucl. Phys. B310(1988)25; H. Hata and Y. Nagoshi, Prog. Theor. Phys. 80(1988) 80; O. Bergman and B. Zwiebach, Nucl. Phys. B441 (1995) 441.
54. K. Becker, M. Becker, J. Polchinski and A. Tseytlin, Phys. Rev. D56(1997) 3174.
55. S. B. Giddings, F. Hacqueboard and H. Verlinde, hep-th/9804121.
56. R. Dijkgraaf, E. Verlinde and H. Verlinde, Nucl. Phys. B500(1997)43.
57. K. Becker and M. Becker, Nucl. Phys. B506(1997)48.
58. Y. Okawa and T. Yoneya, hep-th/9806108.
59. M. Dine and A. Rajaraman, hep-th/9710174. M. Fabbrichesi, G. Ferretti and R. Iengo, hep-th/9806018, hep-th/9806166; W. Taylor IV and M. Van Raamsdonk, hep-th/9806066; R.Echols and J. P. Gray, hep-th/9806109; J. McCarthy, L. Susskind and A. Wilkins, hep-th/9806136.
60. S. Paban, S. Sethi and M. Stern, hep-th/9805018. See also, M. Dine, R. Echols and J. P. Gray, hep-th/9805007.
61. A. Jevicki and T. Yoneya, hep-th/9805069.
62. J. Maldacena, hep-th/9711200; N. Itzhaki, J. Maldacena, J. Sonnenshain and S. Yankielowicz, hep-th/9802042. See also earlier works, S. Gubser, I. Klebanov and A. Peet, Phys. Rev. D54(1996) 3916; I. Klebanov, Nucl. Phys. B496 (1997) 231; S. Gubser, I. Klebanov and A. Tseytlin, Nucl. Phys. B499 (1997) 217.
63. J. Maldacena, hep-th/9711200; N. Itzhaki, J. Maldacena, J. Sonnenshain and S. Yankielowicz, hep-th/9802042. See also earlier works, S. Gubser, I. Klebanov and A. Peet, Phys. Rev. D54(1996) 3916; I. Klebanov, Nucl. Phys. B496 (1997) 231; S. Gubser, I. Klebanov and A. Tseytlin, Nucl. Phys. B499 (1997) 217.
64. J. Maldacena, hep-th/9711200; N. Itzhaki, J. Maldacena, J. Sonnenshain and S. Yankielowicz, hep-th/9802042. See also earlier works, S. Gubser, I. Klebanov and A. Peet, Phys. Rev. D54(1996) 3916; I. Klebanov, Nucl. Phys. B496 (1997) 231; S. Gubser, I. Klebanov and A. Tseytlin, Nucl. Phys. B499 (1997) 217.
65. J. Maldacena, hep-th/9711200; N. Itzhaki, J. Maldacena, J. Sonnenshain and S. Yankielowicz, hep-th/9802042. See also earlier works, S. Gubser, I. Klebanov and A. Peet, Phys. Rev. D54(1996) 3916; I. Klebanov, Nucl. Phys. B496 (1997) 231; S. Gubser, I. Klebanov and A. Tseytlin, Nucl. Phys. B499 (1997) 217.
66. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, hep-th/9802109.
67. E. Witten, hep-th/9802150.
68. A. Jevicki, Y. Kazama and T. Yoneya, to appear.
69. T. Yoneya, Prog. Theor. Phys. 97(1997)949.
70. T. Banks, Fischler, I. R. Klebanov and L. Susskind, Phys. Rev. Lett. 80(1997)226.
71. G. Horowitz and E. Martinec, Phys. Rev. D57(1998)4935.
72. T. Banks, Fischler, I. R. Klebanov and L. Susskind, hep-th/9711005.
73. M. Li and E. Martinec, hep-th/9801070.
74. M. Li, hep-th/9710226.
75. M. Li, E. Martinec and V. Sahakian, to appear.
76. H. Liu and A. A. Tseytlin, hep-th/9712063; D. Lowe, hep-th/9802173; D. Kabat and G. Lifschytz, hep-th/9806214.
77. L. Susskind and E. Witten, hep-th/9805114.
78. D. Minic, private communiation.
79. M. Douglas, hep-th/9610041.
80. A. Conne, M. Douglas and A. Schwarz, hep-th/9711262.
81. S. Hirano and M. Kato, Prog. Theor. Phys. 98(1997) 1371.
82. I. Oda, Nucl. Phys. B516(1998)160.