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Canonical equivalence of non-isometric \(\sigma{}\)-models and Poisson-Lie \(T\)-duality. (English) Zbl 0945.81022
Summary: We prove that a transformation, conjectured in our previous work, between phase-space variables in \(\sigma\)-models related by Poisson-Lie \(T\)-duality is indeed a canonical one. We do so by explicitly demonstrating the invariance of the classical Poisson brackets. This is the first example of a class of \(\sigma\)-models with no isometries related by canonical transformations. In addition we discuss generating functionals of canonical transformations in generally non-isometric, bosonic and supersymmetric \(\sigma\)-models and derive the complete set of conditions that determine them. We apply this general formalism to find the generating functional for Poisson-Lie \(T\)-duality. We also comment on the relevance of this work to \(D\)-brane physics and to quantum aspects of \(T\)-duality.

MSC:
81T10 Model quantum field theories
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[1] Kikkawa, K.; Yamasaki, M.; Sakai, N.; Senda, I.; Buscher, T.; Buscher, T., Phys. lett. B, Prog. theor. phys., Phys. lett. B, Phys. lett. B, 201, 466, (1988)
[2] Giveon, A.; Rabinovici, E.; Veneziano, G.; Meissner, K.; Veneziano, G., Nucl. phys. B, Phys. lett. B, 267, 33, (1991)
[3] Rocek, M.; Verlinde, E.; Giveon, A.; Rocek, M.; Hassan, S.F.; Sen, A.; Henningson, M.; Nappi, C.; Kiritsis, E.; Evans, M.; Giannakis, I., Nucl. phys. B, Nucl. phys. B, Nucl. phys. B, Phys. rev. D, Nucl. phys. B, Nucl. phys. B, 472, 139, (1996), [hep-th/9511061]
[4] N. Mohammedi, Tours Univ. preprint [hep-th/9709071].
[5] Giveon, A.; Porrati, M.; Rabinovici, E.; Alvarez, E.; Alvarez-Gaumé, L.; Lozano, Y., Phys. rep., Nucl. phys. B (proc. suppl.), 1, 1, (1995), [hep-th/9410237]
[6] Curtright, T.L.; Zachos, C.K., Phys. rev. D, 49, 5408, (1994), [hep-th/9401006]
[7] Alvarez, E.; Alvarez-Gaumé, L.; Lozano, Y., Phys. lett. B, 336, 183, (1994), [hep-th/9406206]
[8] Lozano, Y.; Alvarez, O.; Liu, C.-Hao, Phys. lett. B, Commun. math. phys., 179, 185, (1996), hep-th/9503226]
[9] Sfetsos, K., Phys. rev. D, 54, 1682, (1996), [hep-th/9602179]
[10] Klimcik, C.; Severa, P.; Klimcik, C., Phys. lett. B, Nucl. phys. B (proc. suppl.), 46, 116, (1996), [hep-th/9509095]
[11] Klimcik, C.; Severa, P., Phys. lett. B, 372, 65, (1996), [hep-th/9512040]
[12] Sfetsos, K., Nucl. phys. B (proc. suppl.), 56, 302, (1997), [hep-th/9611199]
[13] Bakas, I.; Sfetsos, K.; Hassan, S.F.; Sfetsos, K., Phys. lett. B, Nucl. phys. B, Nucl. phys. B, 463, 33, (1996), [hep-th/9510034]
[14] Polchinski, J., Phys. rev. lett., 75, 4724, (1995), [hep-th/9510017]
[15] Horava, P.; Green, M.B., Phys. lett. B, Phys. lett. B, 266, 325, (1991)
[16] Dai, J.; Leigh, R.G.; Polchinski, J.; Lei, R.G., Mod. phys. lett. A, Mod. phys. lett. A, 4, 2767, (1989)
[17] Fischler, W.; Susskind, L.; Fischler, W.; Susskind, L.; Lovelace, C.; Callan, C.G.; Lovelace, C.; Nappi, C.R.; Yost, S.A., Phys. lett. B, Phys. lett. B, Nucl. phys. B, Nucl. phys. B, 288, 525, (1987)
[18] Alekseev, A.Yu.; Malkin, A.Z., Commun. math. phys., 162, 147, (1994)
[19] E. Tyurin and R. von Unge, Phys. Lett. B 382 233 1 hep-th/9512025].
[20] Alekseev, A.Yu.; Klimcik, C.; Tseytlin, A.A., Nucl. phys. B, 458, 430, (1996), [hep-th/9509123]
[21] Klimcik, C.; Severa, P.; Klimcik, C.; Severa, P., Phys. lett. B, Nucl. phys. B, 488, 653, (1997), [hep-th/9609112]
[22] C. Klimcik, IHES-P-97-58 [hep-th/9707194].
[23] S.E. Parkhomenko, preprint LANDAU-TMP-06-97 [hep-th/9706199]; preprint LANDAU-TMP-09-97 I hep-th/9710037].
[24] O. Alvarez, Published in: Cargese 1995, Low-dimensional applications of quantum field theory, pp. 1-18 [hep-th/95 11024].
[25] Schouten, J.A., Ricci calculus, (1954), Springer Berlin · Zbl 0057.37803
[26] Ghandour, G.; Curtright, T.; Ghandour, G., (), 35, 1289, (1987)
[27] van Nieuwenhuizen, P.; de Wit, B., Nucl. phys. B, 312, 58, (1989)
[28] Curtright, T.L.; Zachos, C.K.; Curtright, T.L.; Uematsu, T.; Zachos, C.; Lozano, Y., Phys. rev. D, Nucl. phys. B, Mod. phys. lett. A, 11, 2893, (1996), [hep-th/9610024]
[29] F. Quevedo, IFUNAM-FT-97-7 [hep-th/9706210].
[30] Bars, I.; Sfetsos, K.; Kiritsis, E.; Obers, N.A.; Tyurin, E., Mod. phys. lett. A, Phys. lett. B, Phys. lett. B, 364, 157, (1995), [hep-th/9507014]
[31] Alvarez, E.; Barbon, J.L.F.; Borlaf, J.; Dorn, H.; Otto, H.J.; Forste, S.; Kehagias, A.A.; Schwager, S.; Borlaf, J.; Lozano, Y., Nucl. phys. B, Phys. lett. B, Nucl. phys. B, Nucl. phys. B, 480, 239, (1996), [hep-th/9607051]
[32] Tseytlin, A.A., Mod. phys. lett. A, 6, 1721, (1991)
[33] L.K. Balazs, J. Balog, P. Forgacs, N. Mohammedi, L. Palla and J. Schnittger, ITP-BUDAPEST-532 [hep-th/9704137].
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