Duval, C.; Hassaïne, M.; Horváthy, P. A. The geometry of Schrödinger symmetry in non-relativistic CFT. (English) Zbl 1162.81034 Ann. Phys. 324, No. 5, 1158-1167 (2009). Summary: The non-relativistic conformal “Schrödinger” symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the “Bargmann framework”. The formalism incorporates the Equivalence Principle. Newton-Hooke conformal symmetries, which are analogs of those of Schrödinger in the presence of a negative cosmological constant, are discussed in a similar way. Further examples include topologically massive gravity with negative cosmological constant and the Madelung hydrodynamical description. Cited in 52 Documents MSC: 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 83E15 Kaluza-Klein and other higher-dimensional theories 81V17 Gravitational interaction in quantum theory 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) Keywords:non-relativistic conformal symmetry; Bargmann framework; Kaluza-Klein type theory; non-relativistic ads/CFT PDFBibTeX XMLCite \textit{C. Duval} et al., Ann. Phys. 324, No. 5, 1158--1167 (2009; Zbl 1162.81034) Full Text: DOI arXiv Link References: [2] Jackiw, R., Phys. Today, 25, 23 (1972) [3] Hagen, C. R., Phys. Rev. D, 5, 377 (1972) [4] Non-relativistic structures were earlier identified in C. Duval, Doctoral Thesis, Marseille, 1982.; Non-relativistic structures were earlier identified in C. Duval, Doctoral Thesis, Marseille, 1982. [5] Duval, C.; Gibbons, G. W.; Horvathy, P. A., Phys. Rev. D, 43, 3907 (1991) [6] de Alfaro, V.; Fubini, S.; Furlan, G., Nuovo Cim. A, 34, 569 (1976) [7] Jackiw, R., Ann. Phys., 129, 183 (1980) [8] Horvathy, P. A., Lett. Math. Phys., 7, 353 (1983) [9] Jackiw, R., Ann. Phys., 201, 83 (1990) [10] Jackiw, R.; Pi, S.-Y., Phys. Rev. D, 42, 3500 (1990) [11] Duval, C.; Horvathy, P.; Palla, L., Ann. Phys., 249, 265 (1996) [12] Hassaïne, M.; Horvathy, P., Phys. Lett. A, 279, 215 (2001) [13] O’Raifeartaigh, L.; Sreedhar, V. V., Ann. Phys., 293, 215 (2001) [14] Henkel, M.; Unterberger, J., Nucl. Phys. B, 660, 407 (2003) [15] Balasubramanian, K.; McGreevy, J., Phys. Rev. Lett., 101, 061601 (2008) [16] Son, D. T., Phys. Rev. D, 78, 046003 (2008) [17] Leiva, C.; Plyushchay, M. S., Ann. Phys. (N.Y.), 307, 372 (2003) [18] A. Akhavan, M. Alishahiha, A. Davody, A. Vahedi, hep-th/0811.3067; A. Akhavan, M. Alishahiha, A. Davody, A. Vahedi, hep-th/0811.3067 [19] Siklos, S. T.C., (MacCallum, M. A.H., Galaxies, Axisymmetric Systems and Relativity (1985), Cambridge University Press: Cambridge University Press Cambridge) [20] Banados, M.; Chamblin, A.; Gibbons, G. W., Phys. Rev. D, 61, 081901(R) (2000) [21] Ayon-Beato, E.; Hassaïne, M., Phys. Rev. D, 75, 064025 (2007) [22] Brinkmann, H. W., Math. Ann., 94, 119 (1925) [23] Einstein, A., Über die Spezielle und die Allgemeine Relativitätstheorie (1921), Vieweg: Vieweg Braunschweig · JFM 46.1279.01 [24] Hasselbach, F.; Nicklaus, M., Phys. Rev. A, 48, 143 (1993), See, e.g. [25] Zimmerman, J. E.; Mercereau, J. E., Phys. Rev. Lett., 14, 887 (1965) [26] F. London, Superfluids, vol. I, Wiley/Chapman & Hall, London, 1950.; F. London, Superfluids, vol. I, Wiley/Chapman & Hall, London, 1950. · Zbl 0041.58507 [27] Brickman, N. F., Phys. Rev., 184, 460 (1969) [28] Avenel, O.; Hakonen, P.; Varoquaux, E., Phys. Rev. Lett., 78, 3602 (1997) [29] Duval, C.; Horváthy, P. A.; Palla, L., Phys. Rev. D, 50, 6658 (1994) [30] Gibbons, G. W.; Patricot, C. E., Class. Quant. Grav., 20, 5225 (2003) [31] Niederer, U., Helv. Phys. Acta, 46, 191 (1973) [32] Burdet, G.; Duval, C.; Perrin, M., Lett. Math. Phys., 10, 255 (1985) [33] Jackiw, R.; Pi, S. Y., Phys. Rev. D, 44, 2524 (1991) [34] Phys. Rev. Lett., 48, 975 (1982) [35] Banados, M.; Teitelboim, C.; Zanelli, J., Phys. Rev. Lett., 69, 1849 (1992) [36] Li, W.; Song, W.; Strominger, A., JHEP, 0804, 082 (2008) [37] Deser, S., (Christensen, S. M., Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. deWitt (1984), Adam Hilger: Adam Hilger London) [38] G.W. Gibbons, C.N. Pope, E. Sezgin, hep-th/0807.2613; G.W. Gibbons, C.N. Pope, E. Sezgin, hep-th/0807.2613 [39] Ayon-Beato, E.; Hassaïne, M., Ann. Phys., 317, 175 (2005) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.