TFD approach to bosonic strings and Dp-branes

International Journal of Modern Physics A

Volumn 18, Issue 12, 2003, Pages 2109-2117

  Abdalla, M C B ^a   Gadelha, A L ^a   Vancea, I V ^b  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

D branes; Finite temperature; Strings

Indexed keywords

CALCULATION; CONFERENCE PAPER; ELEMENTARY PARTICLE; ENTROPY; QUANTUM THEORY; TEMPERATURE; VACUUM;

EID: 0038475925     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X03015556     Document Type: Conference Paper

References (42)

1. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
2. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
3. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
4. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
5. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
6. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
7. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
8. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
9. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
10. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
11. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
12. M. V. Mozo, Phys. Lett. B388, 494 (1996); J. L. F. Barbon and M. V. Mozo, Nucl. Phys. B497, 236 (1997); S. A. Abel, J. L. F. Barbon, I. I. Kogan, E. Rabinovici, J. High Energy Phys. 9904, 015 (1999); J. L. F. Barbon, E. Rabinovici, J. High Energy Phys. 0106, 029 (2001); E. Kiritsis, J. High Energy Phys. 9910, 010 (1999); E. Kiritsis and W. Taylor, hep-th/9906048; G. Dvali, I. I. Kogan and M. Shifman, Phys. Rev. D62, 106001 (2000); S. Abel, K. Freese and I. I. Kogan, J. High Energy Phys. 0101, 039 (2001); I. I. Kogan, A. Kovner and M. Schvellinger, hep-th/0103235; A. Bytsenko, S. Odintsov and L. Granada, Mod. Phys. Lett. A11, 2525 (1996); J. Ambjorn, Yu. Makeenko, G. W. Semenoff and R. Szabo, Phys. Rev. D60, 106009 (1999); S. S. Gubser, I. R. Klebanov, M. Rangamani, E. Witten, hep-th/0009140.
13. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
14. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
15. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
16. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
17. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
18. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
19. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
20. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
21. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
22. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
23. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
24. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
25. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
26. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
27. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
28. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
29. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
30. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
31. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
32. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
33. A. Sen, Nucl. Phys. B440, 421 (1995); A. Strominger and C. Vafa, Phys. Lett. B379, 99 (1996); L. Susskind, hep-th/9309145; G. Horowitz and J. Polchinski, Phys. Rev. D55, 6189 (1997); T. Banks, W. Fischler, I. Klebanov and L. Susskind Phys. Rev. Lett. 80, 226 (1998), J. High Energy Phys. 9801, 008 (1998); S. Chaudhuri and D. Minic, Phys. Lett. B433, 301 (1998); I. Klebanov and L. Susskind, Phys. Lett. B16, 62 (1998); E. Halyo, hep-th/9709225; S. Das, S. Mathur, S. Kalyana Rama and P. Ramadevi, Nucl. Phys. B27, 187 (1998); G. Horowitz and E. Martinec, Phys. Rev. D57, 4935 (1998); M. Li, J. High Energy Phys. 9801, 009 (1998); M. Li and E. Martinec, hep-th/9801070; T. Banks, W. Fischler and I. Klebanov, Phys. Lett. B423, 54 (1998); H. Liu and A. Tseytlin, J. High Energy Phys. 9801, 010 (1998); D. Minic, hep-th/9712202; A. Strominger, Phys. Rev. Lett. 71, 3397 (1993); I. V. Volovich, hep-th/9608137; J. Maldacena and A. Strominger, J. High Energy Phys. 9807, 013 (1998); M. L. Meana and J. P. Peñalba, Nucl. Phys. B560, 154 (1999); S. Mukohyama, Mod. Phys. Lett. A11, 3035 (1996).
34. I. V. Vancea, Phys. Lett. B487, 175 (2000).
35. M. C. B. Abdalla, A. L. Gadelha and I. V. Vancea, Phys. Rev. D64, 086005 (2001).
36. M. C. B. Abdalla, E. Graça and I. V. Vancea, Phys. Lett. B536, 114 (2002).
37. M. C. B. Abdalla, A. L. Gadelha and I. V. Vancea, Phys. Rev. D66, 065005 (2002).
38. Y. Takahashi and H. Umezawa, Collective Phenom. 2, 55 (1975).
39. H. Umezawa, Advanced Field Theory: Micro, Macro and Thermal Field (American Institute of Physics, 1993).
40. M. B. Green, J. H. Shwarz and E. Witten, Superstring Theory (Cambridge University Press, 1987).
41. P. Di Vecchia and A. Liccardo, D-Branes in String Theory, hep-th/9912161, hepth/991227.
42. M. C. B. Abdalla, A. L. Gadelha and I. V. Vancea, Phys. Lett. A273, 235 (2000).