Quantization of the open string on plane-wave limits of dS(n) x S-n and non-commutativity outside branes

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The open string on the plane-wave limit of dSn × Sn with constant B2 and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string world-sheet parameter σ, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski space–time limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.
© 2008 Elsevier B.V. All rights reserved. The authors are grateful to MEC and CAM, Spain for partial support through grants Nos. FIS2005-02309 and UCM-910770. The work of G.H. was supported by an MEC-FPU fellowship.
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[1] R. Penrose, in: M. Cahen, M. Flato (Eds.), Differential Geometry and Relativity, Reidel, Dordrecht, 1976, p. 271. [2] R. Penrose, Rev. Mod. Phys. 37 (1965) 215; For a summary of the geometric properties, see H. Stephani, D. Kramer, M. Maccallum, C. Hoenselaers, E. Herlt, Exact Solutions to Einstein’s Field Equations, second ed., Cambridge Univ. Press, Cambridge, 2003; G.W. Gibbons, Commun. Math. Phys. 45 (1975) 191. [3] D. Amati, C. Klimcik, Phys. Lett. B 219 (1989) 443. [4] G.T. Horowitz, A.R. Steif, Phys. Rev. Lett. 64 (1990) 260. [5] R. Güven, Phys. Lett. B 482 (2000) 255, hep-th/0005061. [6] J. Kowalski-Glikman, Phys. Lett. B 134 (1984) 194. [7] M. Blau, J. Figueroa-O’Farrill, C. Hull, G. Papadopoulos, JHEP 0201 (2002) 047, hep-th/0110242. [8] M. Blau, J. Figueroa-O’Farrill, G. Papadopoulos, Class. Quantum Grav. 19 (2002) 4573, hep-th/0202111. [9] R.R. Metsaev, Nucl. Phys. B 625 (2002) 70, hep th/0112044; R.R. Metsaev, A.A. Tseytlin, Phys. Rev. D 65 (2002) 126004, hep-th/0202109. [10] D.E. Berenstein, J.M. Maldacena, H.S. Nastase, JHEP 0204 (2002) 013, hep-th/0201093. [11] J.G. Russo, A.A. Tseytlin, JHEP 0204 (2002) 021, hep th/0202179. [12] C. Nappi, E. Witten, Phys. Rev. Lett. 71 (1993) 3751, hep-th/9310112. [13] G. Papadopoulos, J.G. Russo, A.A. Tseytlin, Class. Quantum Grav. 20 (2003) 969, hep-th/0211289. [14] H. Fuji, K. Ito, Y. Sekino, JHEP 0211 (2002) 005, hep th/0209004. [15] E. Silverstein, Simple de Sitter solutions, arXiv: 0712.1196 [hep-th]. [16] E. Witten, Quantum gravity in de Sitter space, hep th/0106109. [17] A. Strominger, JHEP 0110 (2001) 034, hep-th/0106113. [18] N. Seiberg, E. Witten, JHEP 9909 (1999) 032, hep th/9908142. [19] C.S. Chu, P.M. Ho, Nucl. Phys. B 550 (1999) 151, hep th/9812219. [20] F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, JHEP 9902 (1999) 016, hep-th/9810072. [21] S. Doplicher, K. Fredenhagen, J. Roberts, Commun. Math. Phys. 172 (1995) 187, hep-th/0303037. [22] C.S. Chu, P.M. Ho, Nucl. Phys. B 636 (2002) 219, hep th/0203186. [23] L. Dolan, C.R. Nappi, Phys. Lett. B 551 (2003) 369, hep-th/0210030. [24] G.T. Horowitz, A.R. Steif, Phys. Rev. D 42 (1990) 1950. [25] J. Polchinski, String Theory, vol. I, Cambridge Univ. Press, Cambridge, 2000. [26] F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, Nucl. Phys. B 576 (2000) 578, hep-th/9906161. [27] C.S. Chu, P.M. Ho, Nucl. Phys. B 568 (2000) 447, hep th/9906192. [28] E. Witten, Commun. Math. Phys. 92 (1984) 455. [29] L.D. Faddeev, R. Jackiw, Phys. Rev. Lett. 60 (1988) 1692. [30] R.J. Szabo, Class. Quantum Grav. 23 (2006) R199, hep th/0606233. [31] S. Marculescu, F. Ruiz Ruiz, Phys. Rev. D 74 (2006) 105004, hep-th/0607201. [32] H. de Vega, N. Sánchez, Phys. Rev. D 45 (1992) 2783; H. de Vega, M. Ramón Medrano, N. Sánchez, Class. Quantum Grav. 10 (1993) 2007