Strings in singular time-dependent backgrounds

Fortschritte der Physik

Volumn 51, Issue 7-8, 2003, Pages 805-823

  Giveon, Amit ^a   Rabinovici, Eliezer ^a   Sever, Amit ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038041172     PISSN: 00158208     EISSN: None     Source Type: Journal    
DOI: 10.1002/prop.200310102     Document Type: Conference Paper

References (62)

1. For example: W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57, 107 (1976).
2. W. Fischler and L. Susskind, Holography and cosmology [arXiv:hep-th/9806039]. R. Bousso, A covariant entropy conjecture, JHEP 9907, 004 (1999) [arXiv:hep-th/9905177].
3. W. Fischler and L. Susskind, Holography and cosmology [arXiv:hep-th/9806039]. R. Bousso, A covariant entropy conjecture, JHEP 9907, 004 (1999) [arXiv:hep-th/9905177].
4. J. M. Maldacena and A. Strominger, Statistical entropy of de Sitter space, JHEP 9802, 014 (1998) [arXiv:gr-qc/9801096]. S. Hawking, J. M. Maldacena, and A. Strominger, DeSitter entropy, quantum entanglement and AdS/CFT, JHEP 0105, 001 (2001) [arXiv:hep-th/0002145]. T. Banks, Cosmological breaking of Supersymmetry?, Int. J. Mod. Phys. A 16, 910 (2001).
5. J. M. Maldacena and A. Strominger, Statistical entropy of de Sitter space, JHEP 9802, 014 (1998) [arXiv:gr-qc/9801096]. S. Hawking, J. M. Maldacena, and A. Strominger, DeSitter entropy, quantum entanglement and AdS/CFT, JHEP 0105, 001 (2001) [arXiv:hep-th/0002145]. T. Banks, Cosmological breaking of Supersymmetry?, Int. J. Mod. Phys. A 16, 910 (2001).
6. J. M. Maldacena and A. Strominger, Statistical entropy of de Sitter space, JHEP 9802, 014 (1998) [arXiv:gr-qc/9801096]. S. Hawking, J. M. Maldacena, and A. Strominger, DeSitter entropy, quantum entanglement and AdS/CFT, JHEP 0105, 001 (2001) [arXiv:hep-th/0002145]. T. Banks, Cosmological breaking of Supersymmetry?, Int. J. Mod. Phys. A 16, 910 (2001).
7. see for example: S. W. Hawking, The chronology protection conjecture, Phys. Rev. D 46, 603 (1992).
8. W. A. Hiscock and D. A. Konkowski, Quantum vacuum energy in Taub - Nut (Newman-Unti-Tamburino) type cosmologies, Phys. Rev. D 26, 1225 (1982).
9. S. Elitzur, A. Giveon, D. Kutasov, and E. Rabinovici, From big bang to big crunch and beyond, JHEP 0206, 017 (2002) [arXiv:hep-th/0204189].
10. S. Elitzur, A. Giveon, and E. Rabinovici, Removing singularities, JHEP 0301, 017 (2003) [arXiv:hep-th/0212242].
11. P. Horava, Some exact solutions of string theory in four-dimensions and five-dimensions, Phys. Lett. B 278, 101 (1992) [arXiv:hep-th/9110067]. C. Kounnas and D. Lust, Cosmological string backgrounds from gauged WZW models, Phys. Lett. B 289, 56 (1992) [arXiv:hep-th/9205046]. A. A. Tseytlin, Exact string solutions and duality [arXiv:hep-th/9407099]. J. Simon, The geometry of null rotation identifications, [arXiv:hep-th/0203201]. A. J. Tolley and N. Turok, Quantum fields in a big crunch/big bang spacetime [arXiv:hep-th/0204091].
12. P. Horava, Some exact solutions of string theory in four-dimensions and five-dimensions, Phys. Lett. B 278, 101 (1992) [arXiv:hep-th/9110067]. C. Kounnas and D. Lust, Cosmological string backgrounds from gauged WZW models, Phys. Lett. B 289, 56 (1992) [arXiv:hep-th/9205046]. A. A. Tseytlin, Exact string solutions and duality [arXiv:hep-th/9407099]. J. Simon, The geometry of null rotation identifications, [arXiv:hep-th/0203201]. A. J. Tolley and N. Turok, Quantum fields in a big crunch/big bang spacetime [arXiv:hep-th/0204091].
13. P. Horava, Some exact solutions of string theory in four-dimensions and five-dimensions, Phys. Lett. B 278, 101 (1992) [arXiv:hep-th/9110067]. C. Kounnas and D. Lust, Cosmological string backgrounds from gauged WZW models, Phys. Lett. B 289, 56 (1992) [arXiv:hep-th/9205046]. A. A. Tseytlin, Exact string solutions and duality [arXiv:hep-th/9407099]. J. Simon, The geometry of null rotation identifications, [arXiv:hep-th/0203201]. A. J. Tolley and N. Turok, Quantum fields in a big crunch/big bang spacetime [arXiv:hep-th/0204091].
14. P. Horava, Some exact solutions of string theory in four-dimensions and five-dimensions, Phys. Lett. B 278, 101 (1992) [arXiv:hep-th/9110067]. C. Kounnas and D. Lust, Cosmological string backgrounds from gauged WZW models, Phys. Lett. B 289, 56 (1992) [arXiv:hep-th/9205046]. A. A. Tseytlin, Exact string solutions and duality [arXiv:hep-th/9407099]. J. Simon, The geometry of null rotation identifications, [arXiv:hep-th/0203201]. A. J. Tolley and N. Turok, Quantum fields in a big crunch/big bang spacetime [arXiv:hep-th/0204091].
15. P. Horava, Some exact solutions of string theory in four-dimensions and five-dimensions, Phys. Lett. B 278, 101 (1992) [arXiv:hep-th/9110067]. C. Kounnas and D. Lust, Cosmological string backgrounds from gauged WZW models, Phys. Lett. B 289, 56 (1992) [arXiv:hep-th/9205046]. A. A. Tseytlin, Exact string solutions and duality [arXiv:hep-th/9407099]. J. Simon, The geometry of null rotation identifications, [arXiv:hep-th/0203201]. A. J. Tolley and N. Turok, Quantum fields in a big crunch/big bang spacetime [arXiv:hep-th/0204091].
16. N. A. Nekrasov, Milne universe, tachyons, and quantum group [arXiv:hep-th/0203112].
17. L. Cornalba and M. S. Costa, A new cosmological scenario in string theory, Phys. Rev. D 66, 066001 (2002) [arXiv:hep-th/0203031].
18. A. Giveon and A. Pasquinucci, On cosmological string backgrounds with toroidal isometries, Phys. Lett. B 294, 162 (1992) [arXiv:hep-th/9208076].
19. 2 string model in curved space-time and exact conformal results, Phys. Lett. B 301, 183 (1993) [arXiv:hep-th/9208001].
20. C. R. Nappi and E. Witten, A closed, expanding universe in string theory, Phys. Lett. B 293, 309 (1992) [arXiv:hep-th/9206078].
21. H. Liu, G. Moore, and N. Seiberg, Strings in a time-dependent orbifold, JHEP 0206, 045 (2002) [arXiv:hep-th/0204168].
22. H. Liu, G. Moore, and N. Seiberg, Strings in time-dependent orbifolds, JHEP 0210, 031 (2002) [arXiv:hep-th/0206182].
23. B. Craps, D. Kutasov, and G. Rajesh, String propagation in the presence of cosmological singularities, JHEP 0206, 053 (2002) [arXiv:hep-th/0205101].
24. for example see: O. Aharony, M. Fabinger, G. T. Horowitz, and E. Silverstein, Clean time-dependent string backgrounds from bubble baths, JHEP 0207, 007 (2002) [arXiv:hep-th/0204158].
25. see for example: A. Sen, Time evolution in open string theory, JHEP 0210, 003 (2002) [arXiv:hep-th/0207105].
26. A. Lawrence, On the instability of 3D null singularities, JHEP 0211, 019 (2002) [arXiv:hep-th/0205288].
27. J. M. Maldacena, Eternal black holes in Anti-de-Sitter,[arXiv:hep-th/0106112].
28. S. W. Hawking and D. N. Page, Thermodynamics of black holes in Anti-De Sitter space, Commun. Math. Phys. 87, 577 (1983). E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998) [arXiv:hep-th/9803131].
29. S. W. Hawking and D. N. Page, Thermodynamics of black holes in Anti-De Sitter space, Commun. Math. Phys. 87, 577 (1983). E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998) [arXiv:hep-th/9803131].
30. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
31. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
32. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
33. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
34. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
35. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
36. A. Giveon and A. D. Shapere, Gauge symmetries of the N = 2 string, Nucl. Phys. B 386, 43 (1992) [arXiv:hep-th/9203008]. G. W. Moore, Finite in all directions [arXiv:hep-th/9305139]. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66, 046005 (2002) [arXiv:hep-th/0109050]. V. Balasubramanian, S. F. Hassan, E. Keski-Vakkuri, and A. Naqvi, A space-time orbifold: A toy model for a cosmological singularity, Phys. Rev. D 67, 026003 (2003) [arXiv:hep-th/0202187]. E. J. Martinec and W. McElgin, Exciting AdS orbifolds [arXiv:hep-th/0206175]. M. Fabinger and J. McGreevy, On smooth time-dependent orbifolds and null singularities [arXiv:hep-th/0206196]. J. Simon, Null orbifolds in AdS, time dependence and holography, JHEP 0210, 036 (2002) [arXiv:hep-th/0208165].
37. J. Figueroa-O'Farrill and J. Simon, Supersymmetric Kaluza-Klein reductions of M2 and M5 branes [arXiv:hep-th/0208107].
38. K. Bardakci and M. B. Halpern, New dual quark models, Phys. Rev. D 3, 2493 (1971). P. Goddard, A. Kent, and D. I. Olive, Virasoro algebras and Coset space models, Phys. Lett. B 152, 88 (1985).
39. K. Bardakci and M. B. Halpern, New dual quark models, Phys. Rev. D 3, 2493 (1971). P. Goddard, A. Kent, and D. I. Olive, Virasoro algebras and Coset space models, Phys. Lett. B 152, 88 (1985).
40. A. B. Zamolodchikov, 'Irreversibility' of the flux of the renormalization group in a 2-d field theory, JETP Lett. 43, 730 (1986) [Zh. Eksp. Teor. Fiz. Pisma Red. 43, 565 (1986)].
41. K. Bardakci, E. Rabinovici, and B. Saering, String models with C < 1 components, Nucl. Phys. B 299, 151 (1988). D. Altschuler, K. Bardakci, and E. Rabinovici, A construction of the C < 1 modular invariant partition functions, Commun. Math. Phys. 118, 241 (1988). W. Nahm, Gauging symmetries of two-dimensional conformally invariant models, UCD-88-02. D. Karabali, Q. H. Park, H. J. Schnitzer, and Z. Yang, A Gko Construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216, 307 (1989). K. Gawedzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320, 625 (1989).
42. K. Bardakci, E. Rabinovici, and B. Saering, String models with C < 1 components, Nucl. Phys. B 299, 151 (1988). D. Altschuler, K. Bardakci, and E. Rabinovici, A construction of the C < 1 modular invariant partition functions, Commun. Math. Phys. 118, 241 (1988). W. Nahm, Gauging symmetries of two-dimensional conformally invariant models, UCD-88-02. D. Karabali, Q. H. Park, H. J. Schnitzer, and Z. Yang, A Gko Construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216, 307 (1989). K. Gawedzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320, 625 (1989).
43. K. Bardakci, E. Rabinovici, and B. Saering, String models with C < 1 components, Nucl. Phys. B 299, 151 (1988). D. Altschuler, K. Bardakci, and E. Rabinovici, A construction of the C < 1 modular invariant partition functions, Commun. Math. Phys. 118, 241 (1988). W. Nahm, Gauging symmetries of two-dimensional conformally invariant models, UCD-88-02. D. Karabali, Q. H. Park, H. J. Schnitzer, and Z. Yang, A Gko Construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216, 307 (1989). K. Gawedzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320, 625 (1989).
44. K. Bardakci, E. Rabinovici, and B. Saering, String models with C < 1 components, Nucl. Phys. B 299, 151 (1988). D. Altschuler, K. Bardakci, and E. Rabinovici, A construction of the C < 1 modular invariant partition functions, Commun. Math. Phys. 118, 241 (1988). W. Nahm, Gauging symmetries of two-dimensional conformally invariant models, UCD-88-02. D. Karabali, Q. H. Park, H. J. Schnitzer, and Z. Yang, A Gko Construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216, 307 (1989). K. Gawedzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320, 625 (1989).
45. K. Bardakci, E. Rabinovici, and B. Saering, String models with C < 1 components, Nucl. Phys. B 299, 151 (1988). D. Altschuler, K. Bardakci, and E. Rabinovici, A construction of the C < 1 modular invariant partition functions, Commun. Math. Phys. 118, 241 (1988). W. Nahm, Gauging symmetries of two-dimensional conformally invariant models, UCD-88-02. D. Karabali, Q. H. Park, H. J. Schnitzer, and Z. Yang, A Gko Construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216, 307 (1989). K. Gawedzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320, 625 (1989).
46. K. Bardacki, M. J. Crescimanno, and E. Rabinovici, Parafermions from coset models, Nucl. Phys. B 344, 344 (1990). E. Witten, On string theory and black holes, Phys. Rev. D 44, 314 (1991).
47. K. Bardacki, M. J. Crescimanno, and E. Rabinovici, Parafermions from coset models, Nucl. Phys. B 344, 344 (1990). E. Witten, On string theory and black holes, Phys. Rev. D 44, 314 (1991).
48. R. Dijkgraaf, H. Verlinde, and E. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371, 269 (1992). A. A. Tseytlin, Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys. B 411, 509 (1994) [arXiv:hep-th/9302083]. H. J. de Vega, A. L. Larsen, and N. Sanchez, Non-singular string-cosmologies from exact conformal field theories, Nucl. Phys. B, Proc. Suppl. 102, 201 (2001) [arXiv:hep-th/0110262].
49. R. Dijkgraaf, H. Verlinde, and E. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371, 269 (1992). A. A. Tseytlin, Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys. B 411, 509 (1994) [arXiv:hep-th/9302083]. H. J. de Vega, A. L. Larsen, and N. Sanchez, Non-singular string-cosmologies from exact conformal field theories, Nucl. Phys. B, Proc. Suppl. 102, 201 (2001) [arXiv:hep-th/0110262].
50. R. Dijkgraaf, H. Verlinde, and E. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371, 269 (1992). A. A. Tseytlin, Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys. B 411, 509 (1994) [arXiv:hep-th/9302083]. H. J. de Vega, A. L. Larsen, and N. Sanchez, Non-singular string-cosmologies from exact conformal field theories, Nucl. Phys. B, Proc. Suppl. 102, 201 (2001) [arXiv:hep-th/0110262].
51. M. Gasperini and G. Veneziano, Pre-big bang in string cosmology, Astropart. Phys. 1, 317 (1993) [arXiv:hep-th/9211021]. R. Brustein and G. Veneziano, The graceful exit problem in string cosmology, Phys. Lett. B 329, 429 (1994) [arXiv:hep-th/9403060]. G. Veneziano, String cosmology: The pre-big bang scenario [arXiv:hep-th/0002094]. J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, and N. Turok, From big crunch to big bang [arXiv:hep-th/0108187].
52. M. Gasperini and G. Veneziano, Pre-big bang in string cosmology, Astropart. Phys. 1, 317 (1993) [arXiv:hep-th/9211021]. R. Brustein and G. Veneziano, The graceful exit problem in string cosmology, Phys. Lett. B 329, 429 (1994) [arXiv:hep-th/9403060]. G. Veneziano, String cosmology: The pre-big bang scenario [arXiv:hep-th/0002094]. J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, and N. Turok, From big crunch to big bang [arXiv:hep-th/0108187].
53. M. Gasperini and G. Veneziano, Pre-big bang in string cosmology, Astropart. Phys. 1, 317 (1993) [arXiv:hep-th/9211021]. R. Brustein and G. Veneziano, The graceful exit problem in string cosmology, Phys. Lett. B 329, 429 (1994) [arXiv:hep-th/9403060]. G. Veneziano, String cosmology: The pre-big bang scenario [arXiv:hep-th/0002094]. J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, and N. Turok, From big crunch to big bang [arXiv:hep-th/0108187].
54. M. Gasperini and G. Veneziano, Pre-big bang in string cosmology, Astropart. Phys. 1, 317 (1993) [arXiv:hep-th/9211021]. R. Brustein and G. Veneziano, The graceful exit problem in string cosmology, Phys. Lett. B 329, 429 (1994) [arXiv:hep-th/9403060]. G. Veneziano, String cosmology: The pre-big bang scenario [arXiv:hep-th/0002094]. J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, and N. Turok, From big crunch to big bang [arXiv:hep-th/0108187].
55. R. Dijkgraaf, H. Verlinde, and E. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371, 269 (1992).
56. N. J. Vilenkin, Special Functions and the Theory of Group Representations (AMS, 1968).
57. P. Kraus, H. Ooguri, and S. Shenker, Inside the horizon with AdS/CFT [arXiv:hep-th/0212277].
58. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998); [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200].
59. G. T. Horowitz and J. Polchinski, Instability of spacelike and null orbifold singularities, Phys. Rev. D 66, 103512 (2002) [arXiv:hep-th/0206228].
60. M. Gasperini, J. Maharana, and G. Veneziano, Boosting away singularities from conformal string backgrounds, Phys. Lett. B 296, 51 (1992) [arXiv:hep-th/9209052].
61. A. Giveon, M. Porrati, and E. Rabinovici, Target space duality in string theory, Phys. Rep. 244, 77 (1994) [arXiv:hep-th/9401139].
62. A. Giveon and M. Rocek, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [arXiv:hep-th/9112070].