Noncommutativity and its freedoms due to the pp-wave and background gauge fields

Modern Physics Letters A

Volumn 18, Issue 30, 2003, Pages 2125-2133

  Kamani, Davoud ^a  

^a INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

Author keywords

Gauge fields; Noncommutativity; pp waves

Indexed keywords

ARTICLE; GAUGE FIELD; MASS; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; PHYSICS; QUANTUM THEORY; THEORY;

EID: 0242354138     PISSN: 02177323     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217732303011836     Document Type: Article

References (40)

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7. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
8. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
9. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
10. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
11. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
12. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
13. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
14. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
15. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
16. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
17. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
18. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
19. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
20. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
21. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
22. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
23. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
24. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
25. D. Berenstein, J. Maldacena and H. Nastase, JHEP 0204, 013 (2002); D. Amati and C. Klimcik, Phys. Lett. B210, 92 (1988); G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990); H. J. de Vega and N. Sanchez, ibid. 65, 1517 (1990), Phys. Lett. B244, 215 (1990); O. Jofre and C. Nunez, Phys. Rev. D50, 5232 (1994); C. R. Nappi and E. Witten, Phys. Rev. Lett. 71, 3751 (1993); E. Kiritsis and C. Kounnas, Phys. Lett. B320, 264 (1994); C. Klimcik and A. A. Tseytlin, ibid. B323, 305 (1994); K. Sfetsos and A. A. Tseytlin, Nucl. Phys. B427, 245 (1994); J. G. Russo and A. A. Tseytlin, ibid. B448, 293 (1995); JHEP 0204, 021 (2002); G. T. Horowitz and A. R. Steif, Phys. Rev. D42, 1950 (1990); G. T. Horowitz and A. A. Tseytlin, ibid. D51, 2896 (1995); R. Brooks, Mod. Phys. Lett. A6, 841 (1991); H. J. de Vega and N. Sanchez, Phys. Rev. D45, 2783 (1992); H. J. de Vega, M. Ramon Medrano and N. Sanchez, Class. Quantum Grav. 10, 2007 (1993); G. Papadopoulos, J. G. Russo and A. A. Tseytlin, hep-th/0211289; J. G. Russo and A. A. Tseytlin, JHEP 0209, 035 (2002); C. S. Chu and P. M. Ho, Nucl. Phys. B636, 141 (2002); D. Kamani, Phys. Lett. B564, 123 (2003); "Strings in the quantized pp-wave backgrounds from membrane", hep-th/0301003.
26. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
27. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
28. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
29. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
30. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
31. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
32. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
33. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
34. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
35. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
36. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
37. N. Seiberg and E. Witten, JHEP 9909, 032 (1999);A. Connes, M. R. Douglas and A. Schwarz, ibid. 9802, 003 (1998); M. R. Douglas and C. Hull, ibid. 9802, 008 (1998); C. S. Chu and P. M. Ho, Nucl. Phys. B550, 151 (1999); B568, 447 (2000); A. Fayyazuddin and M. Zabzine, Phys. Rev. D62, 046004 (2000); P. M. Ho and Y. T. Yeh, Phys. Rev. Lett. 85, 5523 (2000); Y. E. Cheung and M. Krog, Nucl. Phys. B528, 185 (1998); D. Bigatti and L. Susskind, Phys. Rev. D62, 066004 (2000); A. Schwarz, Nucl. Phys. B534, 720 (1998); F. Ardalan, H. Arfaei and M. M. Sheikh-Jabbari, JHEP 9902, 016 (1999); Nucl. Phys. B576, 578 (2000); V. Schomerus, JHEP 9906, 030 (1999); D. Kamani, Phys. Lett. B548, 231 (2002).
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