p-branes, poisson-sigma models and embedding approach to (p + 1)-dimensional gravity

International Journal of Modern Physics A

Volumn 14, Issue 31, 1999, Pages 4881-4914

  Bandos, Igor A ^a   Kummer, Wolfgang ^b  

^a KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000933220     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X99002311     Document Type: Article

References (136)

1. I. Robinson and Y. Neeman, Rev. Mod. Phys. 37, 201 (1965).
2. L. P. Eisenhart, Riemannian Geometry (Princeton University Press, 1949).
3. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
4. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
5. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
6. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
7. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
8. C. Fronsdal, Phys. Rev. 116, 778 (1959); A. Friedmann, Rev. Mod. Phys. 37, 201 (1965); J. Rosen, Rev. Mod. Phys. 37, 204 (1965); R. Penrose, Rev. Mod. Phys. 37, 215 (1965); C. D. Collinson, J. Math. Phys. 8, 1 (1965); 8, 1547 (1965).
9. D. Kramer, H. Stephani, M. Mac-Callum and E. Herlt, Exact Solutions of Einstein Field Equation, ed. E. Schmutzer (Deutcher Verlag der Wissenschaften, Berlin, 1980), and references therein.
10. T. Regge and C. Teitelboim, "General relativity a là string: a progress report," in Proc. First Marcel Grossman Meeting (Trieste, Italy, 1975), ed. R. Ruffini (North-Holland, Amsterdam, 1977), p. 77.
11. M. Pavsic, Class. Quantum Grav. 2, 869 (1985); Phys. Lett. A116, 1 (1986); Nuovo Cimento A95, 297 (1986); Found. Phys. 24, 1495 (1994); Grav. Cosmol. 2, 1 (1996).
12. M. Pavsic, Class. Quantum Grav. 2, 869 (1985); Phys. Lett. A116, 1 (1986); Nuovo Cimento A95, 297 (1986); Found. Phys. 24, 1495 (1994); Grav. Cosmol. 2, 1 (1996).
13. M. Pavsic, Class. Quantum Grav. 2, 869 (1985); Phys. Lett. A116, 1 (1986); Nuovo Cimento A95, 297 (1986); Found. Phys. 24, 1495 (1994); Grav. Cosmol. 2, 1 (1996).
14. M. Pavsic, Class. Quantum Grav. 2, 869 (1985); Phys. Lett. A116, 1 (1986); Nuovo Cimento A95, 297 (1986); Found. Phys. 24, 1495 (1994); Grav. Cosmol. 2, 1 (1996).
15. M. Pavsic, Class. Quantum Grav. 2, 869 (1985); Phys. Lett. A116, 1 (1986); Nuovo Cimento A95, 297 (1986); Found. Phys. 24, 1495 (1994); Grav. Cosmol. 2, 1 (1996).
16. V. Tapia, Class. Quantum Grav. 6, L49 (1989); M. Pavsic, Found. Phys. 26, 159 (1996).
17. V. Tapia, Class. Quantum Grav. 6, L49 (1989); M. Pavsic, Found. Phys. 26, 159 (1996).
18. A. D. Sakharov, Dokl. Akad. Nauk. SSSR 177, 70 (1967); JETP Lett. 12, 1040 (1968); S. L. Adler, Rev. Mod. Phys. 54, 729 (1982), and references therein.
19. A. D. Sakharov, Dokl. Akad. Nauk. SSSR 177, 70 (1967); JETP Lett. 12, 1040 (1968); S. L. Adler, Rev. Mod. Phys. 54, 729 (1982), and references therein.
20. A. D. Sakharov, Dokl. Akad. Nauk. SSSR 177, 70 (1967); JETP Lett. 12, 1040 (1968); S. L. Adler, Rev. Mod. Phys. 54, 729 (1982), and references therein.
21. C. Hull, Nucl. Phys. B468, 113 (1996); J. Schwarz, Nucl. Phys. Proc. Suppl. B55, 1 (1997); K. S. Stelle, "Lectures on supergravity p-branes," hep-th/9701088; P. K. Townsend, "Four lectures on M-theory," hep-th/9612121; "M-theory from its superalgebra," hep-th/9712004, and references therein.
22. C. Hull, Nucl. Phys. B468, 113 (1996); J. Schwarz, Nucl. Phys. Proc. Suppl. B55, 1 (1997); K. S. Stelle, "Lectures on supergravity p-branes," hep-th/9701088; P. K. Townsend, "Four lectures on M-theory," hep-th/9612121; "M-theory from its superalgebra," hep-th/9712004, and references therein.
23. C. Hull, Nucl. Phys. B468, 113 (1996); J. Schwarz, Nucl. Phys. Proc. Suppl. B55, 1 (1997); K. S. Stelle, "Lectures on supergravity p-branes," hep-th/9701088; P. K. Townsend, "Four lectures on M-theory," hep-th/9612121; "M-theory from its superalgebra," hep-th/9712004, and references therein.
24. C. Hull, Nucl. Phys. B468, 113 (1996); J. Schwarz, Nucl. Phys. Proc. Suppl. B55, 1 (1997); K. S. Stelle, "Lectures on supergravity p-branes," hep-th/9701088; P. K. Townsend, "Four lectures on M-theory," hep-th/9612121; "M-theory from its superalgebra," hep-th/9712004, and references therein.
25. C. Hull, Nucl. Phys. B468, 113 (1996); J. Schwarz, Nucl. Phys. Proc. Suppl. B55, 1 (1997); K. S. Stelle, "Lectures on supergravity p-branes," hep-th/9701088; P. K. Townsend, "Four lectures on M-theory," hep-th/9612121; "M-theory from its superalgebra," hep-th/9712004, and references therein.
26. P. K. Townsend, Phys. Lett. B350, 184 (1995); "P-brane democracy," in Particles, Strings and Cosmology - Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Theory (19th), and the PASCOS Interdisciplinary Symposium (5th), Baltimore, MD, 22-25 Mar. 1995. ed. J. Bagger (World Scientific, 1996), p. 484; Phys. Lett. B373, 68 (1996).
27. P. K. Townsend, Phys. Lett. B350, 184 (1995); "P-brane democracy," in Particles, Strings and Cosmology - Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Theory (19th), and the PASCOS Interdisciplinary Symposium (5th), Baltimore, MD, 22-25 Mar. 1995. ed. J. Bagger (World Scientific, 1996), p. 484; Phys. Lett. B373, 68 (1996).
28. P. K. Townsend, Phys. Lett. B350, 184 (1995); "P-brane democracy," in Particles, Strings and Cosmology - Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Theory (19th), and the PASCOS Interdisciplinary Symposium (5th), Baltimore, MD, 22-25 Mar. 1995. ed. J. Bagger (World Scientific, 1996), p. 484; Phys. Lett. B373, 68 (1996).
29. I. A. Bandos, Mod. Phys. Lett. A12, 799 (1997).
30. C. Vafa, Nucl. Phys. B469, 403 (1996); D. Kutasov and E. Martinec, Nucl. Phys. B477, 652 (1996); D. Kutasov, E. Martinec and M. O'Loughlin, Nucl. Phys. B477, 675 (1996); A. Lowrence, Class. Quantum Grav. 14, 309 (1997).
31. C. Vafa, Nucl. Phys. B469, 403 (1996); D. Kutasov and E. Martinec, Nucl. Phys. B477, 652 (1996); D. Kutasov, E. Martinec and M. O'Loughlin, Nucl. Phys. B477, 675 (1996); A. Lowrence, Class. Quantum Grav. 14, 309 (1997).
32. C. Vafa, Nucl. Phys. B469, 403 (1996); D. Kutasov and E. Martinec, Nucl. Phys. B477, 652 (1996); D. Kutasov, E. Martinec and M. O'Loughlin, Nucl. Phys. B477, 675 (1996); A. Lowrence, Class. Quantum Grav. 14, 309 (1997).
33. C. Vafa, Nucl. Phys. B469, 403 (1996); D. Kutasov and E. Martinec, Nucl. Phys. B477, 652 (1996); D. Kutasov, E. Martinec and M. O'Loughlin, Nucl. Phys. B477, 675 (1996); A. Lowrence, Class. Quantum Grav. 14, 309 (1997).
34. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
35. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
36. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
37. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
38. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
39. E. Martinec, "Geometrical Structure of M-theory," hep-th/9608017; I. Bars, Phys. Rev. D54, 5203 (1996); Phys. Rev. D55, 2373 (1997); I. Bars and C. Kounnas, Phys. Rev. Lett. 77, 428 (1996); Phys. Rev. D56, 3664 (1997); I. Bars and C. Deliduman, Phys. Lett. B417, 240 (1998), and references therein.
40. M. Janet, Ann. Soc. Polon. Math. 5, 38 (1926); E. Cartan, Ann. Soc. Polon. Math. 6, 1 (1927); A. Freedman, J. Math. Mech. 10, 62 (1961); J. Nash, Ann. Math. 63, 20 (1956); C. J. Clarke, Proc. R. Soc. A314, 417 (1970).
41. M. Janet, Ann. Soc. Polon. Math. 5, 38 (1926); E. Cartan, Ann. Soc. Polon. Math. 6, 1 (1927); A. Freedman, J. Math. Mech. 10, 62 (1961); J. Nash, Ann. Math. 63, 20 (1956); C. J. Clarke, Proc. R. Soc. A314, 417 (1970).
42. M. Janet, Ann. Soc. Polon. Math. 5, 38 (1926); E. Cartan, Ann. Soc. Polon. Math. 6, 1 (1927); A. Freedman, J. Math. Mech. 10, 62 (1961); J. Nash, Ann. Math. 63, 20 (1956); C. J. Clarke, Proc. R. Soc. A314, 417 (1970).
43. M. Janet, Ann. Soc. Polon. Math. 5, 38 (1926); E. Cartan, Ann. Soc. Polon. Math. 6, 1 (1927); A. Freedman, J. Math. Mech. 10, 62 (1961); J. Nash, Ann. Math. 63, 20 (1956); C. J. Clarke, Proc. R. Soc. A314, 417 (1970).
44. M. Janet, Ann. Soc. Polon. Math. 5, 38 (1926); E. Cartan, Ann. Soc. Polon. Math. 6, 1 (1927); A. Freedman, J. Math. Mech. 10, 62 (1961); J. Nash, Ann. Math. 63, 20 (1956); C. J. Clarke, Proc. R. Soc. A314, 417 (1970).
45. R. E. Greene, Mem. Am. Math. Soc. 97, 1 (1970).
46. F. Lund and T. Regge, Phys. Rev. D14, 1524 (1976); R. Omnes, Nucl. Phys. B149, 269 (1979).
47. F. Lund and T. Regge, Phys. Rev. D14, 1524 (1976); R. Omnes, Nucl. Phys. B149, 269 (1979).
48. I. Bandos, P. Pasti, D. Sorokin, M. Tonin and D. Volkov, Nucl. Phys. B446, 79 (1995).
49. I. A. Bandos and A. A. Zheltukhin, JETP Lett. 54, 421 (1991); Phys. Lett. B288, 77 (1992); Sov. J. Nucl. Phys. 56, 198 (1993); J. Elem. Part. Atom. Nucl. 25, 453 (1994).
50. I. A. Bandos and A. A. Zheltukhin, JETP Lett. 54, 421 (1991); Phys. Lett. B288, 77 (1992); Sov. J. Nucl. Phys. 56, 198 (1993); J. Elem. Part. Atom. Nucl. 25, 453 (1994).
51. I. A. Bandos and A. A. Zheltukhin, JETP Lett. 54, 421 (1991); Phys. Lett. B288, 77 (1992); Sov. J. Nucl. Phys. 56, 198 (1993); J. Elem. Part. Atom. Nucl. 25, 453 (1994).
52. I. A. Bandos and A. A. Zheltukhin, JETP Lett. 54, 421 (1991); Phys. Lett. B288, 77 (1992); Sov. J. Nucl. Phys. 56, 198 (1993); J. Elem. Part. Atom. Nucl. 25, 453 (1994).
53. A. Zheltukhin, Sov. J. Nucl. Phys. 33, 1723 (1981); Theor. Math. Phys. 52, 73 (1982); Phys. Lett. B116, 147 (1982); Theor. Math. Phys. 56, 230 (1983).
54. A. Zheltukhin, Sov. J. Nucl. Phys. 33, 1723 (1981); Theor. Math. Phys. 52, 73 (1982); Phys. Lett. B116, 147 (1982); Theor. Math. Phys. 56, 230 (1983).
55. A. Zheltukhin, Sov. J. Nucl. Phys. 33, 1723 (1981); Theor. Math. Phys. 52, 73 (1982); Phys. Lett. B116, 147 (1982); Theor. Math. Phys. 56, 230 (1983).
56. A. Zheltukhin, Sov. J. Nucl. Phys. 33, 1723 (1981); Theor. Math. Phys. 52, 73 (1982); Phys. Lett. B116, 147 (1982); Theor. Math. Phys. 56, 230 (1983).
57. I. A. Bandos, D. Sorokin and D. Volkov, Phys. Lett. B352, 269 (1995).
58. I. Bandos, D. Sorokin and M. Tonin, Nucl. Phys. B497, 275 (1997).
59. I. Bandos, P. Pasti, D. Sorokin and M. Tonin, in: Supersymmetry and Quantum field Theory - Proc. D. Volkov Memorial Seminar (Kharkov, Jan. 5-7, 1997); Lectures Notes in Physics 509, 79 (1998).
60. I. Bandos, P. Pasti, D. Sorokin and M. Tonin, in: Supersymmetry and Quantum field Theory - Proc. D. Volkov Memorial Seminar (Kharkov, Jan. 5-7, 1997); Lectures Notes in Physics 509, 79 (1998).
61. T. Strobl, Phys. Rev. D50, 7356 (1994); P. Schauer and T. Strobl, Mod. Phys. Lett. A9, 3129 (1994).
62. T. Strobl, Phys. Rev. D50, 7356 (1994); P. Schauer and T. Strobl, Mod. Phys. Lett. A9, 3129 (1994).
63. M. O. Katanaev, W. Kummer and H. Liebl, Phys. Rev. D53, 5609 (1996).
64. A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky and E. Sokatchev, Class. Quantum Grav. 1, 498 (1984); Class. Quantum Grav. 2, 155 (1985).
65. A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky and E. Sokatchev, Class. Quantum Grav. 1, 498 (1984); Class. Quantum Grav. 2, 155 (1985).
66. E. Sokatchev, Phys. Lett. B169, 209 (1987); Class. Quantum Grav. 4, 237 (1987) and references in Ref. 17.
67. E. Sokatchev, Phys. Lett. B169, 209 (1987); Class. Quantum Grav. 4, 237 (1987) and references in Ref. 17.
68. M. Green, J. Schwarz and E. Witten, Superstring Theory, Vols. 1 and 2 (Cambridge University Press, Cambridge, 1987).
69. B. M. Barabashov and V. V. Nesterenko, Introduction to the Relativistic String Theory (World Scientific, 1990).
70. A. A. Zheltukhin, Phys. Lett. B233, 112 (1989).
71. I. Bakas and K. Sfetsos, Phys. Rev. D54, 3995 (1996).
72. B. M. Barabashov and V. V. Nesterenko, Commun. Math. Phys. 78, 499 (1981).
73. I. A. Bandos, Phys. Lett. B388, 35 (1996).
74. I. A. Bandos and A. A. Zheltukhin, Class. Quantum Grav. 12, 609 (1995).
75. M. D. Maia, Class. Quantum Grav. 6, 173 (1989).
76. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
77. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
78. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
79. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
80. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
81. E. Sezgin, Phys. Lett. B403, 265 (1997); H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996); H. Nishino, Nucl. Phys. B523, 450 (1998); I. Bars, Phys. Lett. B403, 257 (1997); E. Sezgin and I. Rudichev, "D > 11 superparticle," hep-th/9711128; E. Sezgin, I. Rudichev and P. Sundell, Nucl. Phys. Proc. Suppl. 68, 285 (1998), and references therein.
82. R. I. Nepomechie, Phys. Rev. D31, 1921 (1985); C. Teitelboim, Phys. Lett. B167, 63 (1986).
83. R. I. Nepomechie, Phys. Rev. D31, 1921 (1985); C. Teitelboim, Phys. Lett. B167, 63 (1986).
84. W. Kummer, "Unified treatment of all (1 + 1)-dimensional gravitation models," in Proc. Int. Europhys. Conf. on High Energy Physics (Brussels, 1995), eds. J. Lemonne, C. V. Velde and F. Verbeure (World Scientific, Singapore, 1995), p. 99; W. Kummer and P. Widerin, Phys. Rev. D52, 6965 (1995); M. O. Katanaev, W. Kummer and H. Liebl, Nucl. Phys. B486, 353 (1997).
85. W. Kummer, "Unified treatment of all (1 + 1)-dimensional gravitation models," in Proc. Int. Europhys. Conf. on High Energy Physics (Brussels, 1995), eds. J. Lemonne, C. V. Velde and F. Verbeure (World Scientific, Singapore, 1995), p. 99; W. Kummer and P. Widerin, Phys. Rev. D52, 6965 (1995); M. O. Katanaev, W. Kummer and H. Liebl, Nucl. Phys. B486, 353 (1997).
86. W. Kummer, "Unified treatment of all (1 + 1)-dimensional gravitation models," in Proc. Int. Europhys. Conf. on High Energy Physics (Brussels, 1995), eds. J. Lemonne, C. V. Velde and F. Verbeure (World Scientific, Singapore, 1995), p. 99; W. Kummer and P. Widerin, Phys. Rev. D52, 6965 (1995); M. O. Katanaev, W. Kummer and H. Liebl, Nucl. Phys. B486, 353 (1997).
87. H. Grosse, W. Kummer, P. Prešnajder and D. J. Schwarz, J. Math. Phys. 33, 3892 (1992).
88. F. Haider and W. Kummer, Int. J. Mod. Phys. A9, 207 (1994); W. Kummer, H. Liebl and D. Vassilevich, Nucl. Phys. B493, 491 (1997).
89. F. Haider and W. Kummer, Int. J. Mod. Phys. A9, 207 (1994); W. Kummer, H. Liebl and D. Vassilevich, Nucl. Phys. B493, 491 (1997).
90. P. Thomi, B. Isaak and P. Hajicek, Phys. Rev. D30, 1168 (1984); P. Hajicek, Phys. Rev. D30, 1178 (1984); W. Kummer and S. Lau, Ann. Phys. (N.Y.) 258, 37 (1997).
91. P. Thomi, B. Isaak and P. Hajicek, Phys. Rev. D30, 1168 (1984); P. Hajicek, Phys. Rev. D30, 1178 (1984); W. Kummer and S. Lau, Ann. Phys. (N.Y.) 258, 37 (1997).
92. P. Thomi, B. Isaak and P. Hajicek, Phys. Rev. D30, 1168 (1984); P. Hajicek, Phys. Rev. D30, 1178 (1984); W. Kummer and S. Lau, Ann. Phys. (N.Y.) 258, 37 (1997).
93. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
94. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
95. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
96. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
97. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
98. G. Mandal, A. Sengupta and S. R. Wadia, Mod. Phys. Lett. A6, 1685 (1991); E. Witten, Phys. Rev. D44, 314 (1991); C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D45, 1005 (1992); J. Russo, L. Susskind and L. Thorlacius, Phys. Lett. B292, 13 (1992); T. Banks, A. Dabholkar, M. Douglas and M. O'Laughling, Phys. Rev. D45, 3607 (1992); S. P. de Alwis, Phys. Lett. B289, 278 (1992).
99. C. Teitelboim, Phys. Lett. B126, 41 (1983); R. Jackiw, in Quantum Theory of Gravity, ed. S. Christensen (Higler, Bristol, 1984), p. 403; M. Henneaux, Phys. Rev. Lett. 54, 959 (1985), and second reference in Ref. 39.
100. C. Teitelboim, Phys. Lett. B126, 41 (1983); R. Jackiw, in Quantum Theory of Gravity, ed. S. Christensen (Higler, Bristol, 1984), p. 403; M. Henneaux, Phys. Rev. Lett. 54, 959 (1985), and second reference in Ref. 39.
101. C. Teitelboim, Phys. Lett. B126, 41 (1983); R. Jackiw, in Quantum Theory of Gravity, ed. S. Christensen (Higler, Bristol, 1984), p. 403; M. Henneaux, Phys. Rev. Lett. 54, 959 (1985), and second reference in Ref. 39.
102. G. T. Horwitz and A. Strominger, Nucl. Phys. B360, 197 (1991); S. S. Gubser, I. R. Klebanov and A. W. Peet, Phys. Rev. D54, 3915 (1996); P. K. Townsend, Phys. Lett. B409, 131 (1997); M. Cederwall and P. K. Townsend, J. High Energy Phys. 9, 3 (1997).
103. G. T. Horwitz and A. Strominger, Nucl. Phys. B360, 197 (1991); S. S. Gubser, I. R. Klebanov and A. W. Peet, Phys. Rev. D54, 3915 (1996); P. K. Townsend, Phys. Lett. B409, 131 (1997); M. Cederwall and P. K. Townsend, J. High Energy Phys. 9, 3 (1997).
104. G. T. Horwitz and A. Strominger, Nucl. Phys. B360, 197 (1991); S. S. Gubser, I. R. Klebanov and A. W. Peet, Phys. Rev. D54, 3915 (1996); P. K. Townsend, Phys. Lett. B409, 131 (1997); M. Cederwall and P. K. Townsend, J. High Energy Phys. 9, 3 (1997).
105. G. T. Horwitz and A. Strominger, Nucl. Phys. B360, 197 (1991); S. S. Gubser, I. R. Klebanov and A. W. Peet, Phys. Rev. D54, 3915 (1996); P. K. Townsend, Phys. Lett. B409, 131 (1997); M. Cederwall and P. K. Townsend, J. High Energy Phys. 9, 3 (1997).
106. C. Montonen and D. Olive, Phys. Lett. B72, 117 (1977).
107. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
108. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
109. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
110. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
111. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
112. M. Cederwall, A. von Gussich, B. E. W. Nilsson and A. Westerberg, Phys. Lett. B390, 148 (1997); Nucl. Phys. B490, 163 (1997); M. Cederwall, A. von Gussich, B. E. W. Nilsson, P. Sundell and A. Westerberg, Nucl. Phys. B490, 179 (1997); M. Aganagic, C. Popescu and J. H. Schwarz, Phys. Lett. B393, 311 (1997); Nucl. Phys. B495, 99 (1997); E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).
113. G. Dvali and M. Shifman, Nucl. Phys. B504, 127 (1997).
114. V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B125, 136 (1983).
115. G. W. Gibbons and D. L. Wiltshire, Nucl. Phys. B287, 717 (1987).
116. P. S. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997).
117. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
118. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
119. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
120. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
121. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
122. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
123. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
124. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
125. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
126. P. Howe and E. Sezgin, Phys. Lett. B394, 62 (1997); M. Perry and J. H. Schwarz, Nucl. Phys. B489, 47 (1997); J. H. Schwarz, Phys. Lett. B395, 191 (1997); P. Pasti, D. Sorokin and M. Tonin, Phys. Lett. B398, 41 (1997); I. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. Sorokin and M. Tonin, Phys. Rev. Lett. 78, 4332 (1997); Phys. Lett. B408, 135 (1997); M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, Nucl. Phys. B496, 191 (1997); P. S. Howe, E. Sezgin and P. C. West, Phys. Lett. B399, 49 (1997); Phys. Lett. B400, 255 (1997); T. Adawi, M. Cederwall, U. Gran, M. Holm and B. E. W. Nilsson, Int. J. Mod. Phys. A13, 4691 (1998).
127. S. F. Hewson, M. J. Perry, Nucl. Phys. B492, 249 (1997).
128. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
129. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
130. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
131. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
132. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
133. E. Cremmer and B. Julia, Phys. Lett. B80, 48 (1978); Nucl. Phys. B159, 141 (1979); J. Ellis, M. K. Gaillard and B. Zumino, Phys. Lett. B94, 343 (1980) and references therein; A. D'Adda, P. Di Vecchia and M. Lucher, Nucl. Phys. B146, 63 (1978); B152, 125 (1979); E. Witten, Nucl. Phys. B149, 285 (1979).
134. I. Bandos, D. Sorokin and D. Volkov, Phys. Lett. B372, 77 (1996); I. A. Bandos, "Doubly supersymmetric geometric approach for heterotic string: from generalized action principle to exactly solvable nonlinear equations," in Methods in Mathematical Physics - Proc. 12th Hutsulian Workshop, Rahiv 11-17 Sept. 1995, ed. S. S. Moskaliuk (Palm Harbor, Hadronic Pr., 1997), pp. 33-58.
135. I. Bandos, D. Sorokin and D. Volkov, Phys. Lett. B372, 77 (1996); I. A. Bandos, "Doubly supersymmetric geometric approach for heterotic string: from generalized action principle to exactly solvable nonlinear equations," in Methods in Mathematical Physics - Proc. 12th Hutsulian Workshop, Rahiv 11-17 Sept. 1995, ed. S. S. Moskaliuk (Palm Harbor, Hadronic Pr., 1997), pp. 33-58.
136. M. Chaichian and P. P. Kulish, Phys. Lett. B78, 413 (1978).