The geometry of Schrödinger symmetry in non-relativistic CFT

Annals of Physics

Volumn 324, Issue 5, 2009, Pages 1158-1167

  Duval, C ^a   Hassaine M ^b   Horvathy P A ^c  

^a CNRS   (France)

^b UNIVERSIDAD DE TALCA   (Chile)

^c UNIVERSITÉ DE TOURS   (France)

Author keywords

Bargmann framework; Kaluza Klein type theory; Non relativistic AdS CFT; Non relativistic conformal symmetry

Indexed keywords

EID: 62949216502     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2009.01.006     Document Type: Article

References (64)

1. Jackiw R. Phys. Today 25 (1972) 23
2. Niederer U. Helv. Phys. Acta 45 (1972) 802
3. Hagen C.R. Phys. Rev. D 5 (1972) 377
4. Duval C., Burdet G., Künzle H.P., and Perrin M. Phys. Rev. D 31 (1985) 1841
5. Non-relativistic structures were earlier identified in C. Duval, Doctoral Thesis, Marseille, 1982.
6. Duval C., Gibbons G.W., and Horvathy P.A. Phys. Rev. D 43 (1991) 3907
7. de Alfaro V., Fubini S., and Furlan G. Nuovo Cim. A 34 (1976) 569
8. Jackiw R. Ann. Phys. 129 (1980) 183
9. Horvathy P.A. Lett. Math. Phys. 7 (1983) 353
10. Jackiw R. Ann. Phys. 201 (1990) 83
11. Jackiw R., and Pi S.-Y. Phys. Rev. D 42 (1990) 3500
12. Duval C., Horvathy P., and Palla L. Phys. Lett. B 325 (1994) 39. hep-th/9401065
13. Duval C., Horvathy P., and Palla L. Ann. Phys. 249 (1996) 265. hep-th/9510114
14. Hassaïne M., and Horvathy P. Ann. Phys. (N.Y.) 282 (2000) 218. math-ph/9904022
15. Hassaïne M., and Horvathy P. Phys. Lett. A 279 (2001) 215. hep-th/0009092
16. O'Raifeartaigh L., and Sreedhar V.V. Ann. Phys. 293 (2001) 215. hep-th/0007199
17. Henkel M., and Unterberger J. Nucl. Phys. B 660 (2003) 407. hep-th/0302187
18. Balasubramanian K., and McGreevy J. Phys. Rev. Lett. 101 (2008) 061601
19. Son D.T. Phys. Rev. D 78 (2008) 046003
20. Leiva C., and Plyushchay M.S. Ann. Phys. (N.Y.) 307 (2003) 372
21. W.D. Goldberger, hep-th/0806.2867.
22. J.L.B. Barbon, C.A. Fuertes, hep-th/0806.3244.
23. C.P. Herzog, M. Rangamani, S.F. Ross, hep-th/0807.1099.
24. J. Maldacena, D. Martelli, Y. Tachikawa, hep-th/0807.1100.
25. A. Adams, K. Balasubramanian, J. McGreevy, hep-th/0807.1111.
26. A.V. Galajinsky, hep-th/0808.1553.
27. F.L. Lin, S.Y. Wu, hep-th/0810.0227.
28. S. Sachdev, M. Mueller, cond-mat.str-el/0810.3005.
29. M. Schvellinger, hep-th/0810.3011.
30. L. Mazzucato, Y. Oz, S. Theisen, hep-th/0810.3673.
31. R.C. Myers, M.C. Wapler, hep-th/0811.0480.
32. M. Rangamani, S.F. Ross, D.T. Son, E.G. Thompson, hep-th/0811.2049.
33. A. Akhavan, M. Alishahiha, A. Davody, A. Vahedi, hep-th/0811.3067.
34. Siklos S.T.C. In: MacCallum M.A.H. (Ed). Galaxies, Axisymmetric Systems and Relativity (1985), Cambridge University Press, Cambridge
35. Banados M., Chamblin A., and Gibbons G.W. Phys. Rev. D 61 (2000) 081901R
36. Ayon-Beato E., and Hassaïne M. Phys. Rev. D 75 (2007) 064025. hep-th/0612068
37. Brinkmann H.W. Math. Ann. 94 (1925) 119
38. Einstein A. Über die Spezielle und die Allgemeine Relativitätstheorie (1921), Vieweg, Braunschweig
39. Sagnac G. C.R.A.S. 157 (1913) 708
40. C.R.A.S. 157 (1913) 1410
41. J. Phys. (Paris) 4 (1914) 177
42. See, e.g. Hasselbach F., and Nicklaus M. Phys. Rev. A 48 (1993) 143
43. Zimmerman J.E., and Mercereau J.E. Phys. Rev. Lett. 14 (1965) 887
44. F. London, Superfluids, vol. I, Wiley/Chapman & Hall, London, 1950.
45. Hildebrandt A.F. Phys. Rev. Lett. 12 (1964) 190
46. Brickman N.F. Phys. Rev. 184 (1969) 460
47. Avenel O., Hakonen P., and Varoquaux E. Phys. Rev. Lett. 78 (1997) 3602
48. Duval C., Horváthy P.A., and Palla L. Phys. Rev. D 50 (1994) 6658. hep-ph/9405229
49. Gibbons G.W., and Patricot C.E. Class. Quant. Grav. 20 (2003) 5225. hep-th/0308200
50. Niederer U. Helv. Phys. Acta 46 (1973) 191
51. Burdet G., Duval C., and Perrin M. Lett. Math. Phys. 10 (1985) 255
52. Jackiw R., and Pi S.Y. Phys. Rev. D 44 (1991) 2524
53. Deser S., Jackiw R., and Templeton S. Ann. Phys. 140 (1982) 372 [Erratum-ibid. 185, 406.1988 APNYA,281,409 (1988 APNYA,281,409-449.2000)]
54. Phys. Rev. Lett. 48 (1982) 975
55. Banados M., Teitelboim C., and Zanelli J. Phys. Rev. Lett. 69 (1992) 1849. hep-th/9204099
56. Li W., Song W., and Strominger A. JHEP 0804 (2008) 082. hep-th/0801.4566
57. Deser S., and Kay J.H. Phys. Lett. B 120 (1983) 97
58. Deser S. In: Christensen S.M. (Ed). Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. deWitt (1984), Adam Hilger, London
59. G.W. Gibbons, C.N. Pope, E. Sezgin, hep-th/0807.2613.
60. Ayon-Beato E., and Hassaïne M. Ann. Phys. 317 (2005) 175. hep-th/0409150
61. For a monopole, ds + A · d y is a U (1) connection form on the Hopf bundle.
62. 2. Such an action would again be an isometry of the rescaled metric. It seems that this is not the action people are interested in, however.
63. x.
64. The transformation (40) can be extended to uniform magnetic and electric field, and a curl-free "Aharonov-Bohm" potential [28]. The map (17) does the same for the linear force field.