Maximal supergravities and the e10 coset model

International Journal of Modern Physics D

Volumn 15, Issue 10, 2006, Pages 1619-1642

  Kleinschmidt, Axel ^a   Nicolai, Hermann ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Kac Moody symmetries; Supergravity; Supersymmetry

Indexed keywords

EID: 33750436594     PISSN: 02182718     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218271806009005     Document Type: Article

References (75)

1. E. Cremmer, B. Julia and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76, 409-412 (1978).
2. E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159, 141 (1979).
3. B. Julia, Application of supergravity to gravitation theories, in Unified Field Theories of More Than 4 Dimensions, eds. V. De Sabbata and E. Schmutzer (World Scientific, Singapore, 1983).
4. B. Julia, in Lectures in Applied Mathematics, Vol. 21 (1985), AMS-SIAM, p. 335 [preprint LPTENS 80/16].
5. H. Nicolai, The integrability of N = 16 supergravity, Phys. Lett. B 194, 402 (1987).
6. 10 symmetry in one-dimensional supergravity, Nucl. Phys. B 528, 238-264 (1998) [hep-th/9703160].
7. 10 and arithmetical chaos in superstring cosmology, Phys. Rev. Lett. 86, 4749 (2001) [hep-th/0012172].
8. T. Damour, M. Henneaux and H. Nicolai, Cosmological billiards, Class. Quant. Grav. 20, R145-R200 (2003) [hep-th/0212256].
9. 10 and a "small tension expansion" of M-theory, Phys. Rev. Lett. 89, 221601 (2002) [hep-th/0207267].
10. 9 levels, in Group Theoretical Methods in Physics, Institute of Physics Conference Series No. 185 (IoP Publishing, 2005) [hep-th/0410245].
11. 10 and SO(9,9) invariant supergravity, J. High Energy Phys. 0407, 041 (2004) [hep-th/0407101].
12. 10, Phys. Lett. B 606, 391 (2005) [hep-th/0411225].
13. 10, Class. Quant. Grav. 22, 2849-2879 (2005) hep-th/0504153.
14. 10: billiards, branes and imaginary roots, hep-th/0401053.
15. 10 orbifolds, J. High Energy Phys. 0506, 057 (2005) [hep-th/0409037].
16. P. C. West, Hidden superconformal symmetry in M-theory, J. High Energy Phys. 0008, 007 (2000) [hep-th/0005270].
17. 11 and M-theory, Class. Quant. Grav. 18, 4443-4460 (2001) [hep-th/0104081].
18. A. B. Borisov and V. I. Ogievetsky, Theory of dynamical affine and conformal symmetries as gravity theory, Theor. Math. Phys. 23, 1179-1188 (1976).
19. 11, SL(32) and central charges, Phys. Lett. B 575, 333-342 (2003) [hepth/0307098].
20. +++ invariant formulation of gravity and M-theories: exact BPS solutions, J. High Energy Phys. 0401, 002 (2004) [hep-th/0311255].
21. +++ and the role of space-time, J. High Energy Phys. 0402, 033 (2004) [hep-th/0312247].
22. 11: sign of the times, hep-th/0402090.
23. S. de Buyl, L. Houart and N. Tabti, Dualities and signatures of Q invariant theories, J. High Energy Phys. 0506, 084 (2005) [hep-th/0505199].
24. C. M. Hull, Duality and the signature of space-time, J. High Energy Phys. 9811, 017 (1998) [hep-th/9807127].
25. F. Englert, M. Henneaux and L. Houart, From very-extended to overextended gravity and M-theories, J. High Energy Phys. 0502, 070 (2005) [hep-th/0412184].
26. L Schnakenburg and P. C. West, Kac-Moody symmetries of IIB supergravity, Phys. Lett. B 517, 421-428 (2001) [hep-th/0107081].
27. I. Schnakenburg and P. C. West, Massive IIA supergravity as a nonlinear realization, Phys. Lett. B 540, 137-145 (2002) [hep-th/0204207].
28. K. Bautier, S. Deser, M. Henneaux and D. Seminara, Phys. Lett. B 406, 49-53 (1997) [hep-th/9704131].
29. V. G. Kac, Infinite Dimensional Lie Algebras, 3rd edn. (Cambridge University Press, 1990).
30. R. V. Moody and A. Pianzola, Lie Algebras with Triangular Decomposition (John Wiley & Sons, New York, 1995).
31. n, Class. Quant. Grav. 22, 4457 (2005) [hep-th/0506238].
32. 11, in Proceedings of the Ramanujan International Symposium on Kac-Moody Algebras and Applications, ISKMAA-2002, Chennai, India, 28-31 January [hep-th/0301017].
33. 10 representation at low levels, Nucl. Phys. B 677, 553-586 (2004) [hep-th/0304246].
34. M. R. Gaberdiel, D. I. Olive and P. West, A class of Lorentzian Kac-Moody algebras, Nucl. Phys. B 645, 403-437 (2002) [hep-th/0205068].
35. 8 at low levels, gravity and supergravity, Class. Quant. Grav. 20, 2393-2406 (2003) [hep-th/0212291].
36. A. Kleinschmidt, I. Schnakenburg and P. West, Very-extended Kac-Moody algebras and their interpretation at low levels, Class. Quant. Grav. 21, 2493 (2004) [hep-th/0309198].
37. 11, ten forms and supergravity, hep-th/0511153.
38. E. A. Bergshoeff, M. de Roo, S. F. Kerstan and F. Riccioni, IIB supergravity revisited, J. High Energy Phys. 0508, 098 (2005) [hep-th/0506013].
39. E. A. Bergshoeff, M. de Roo, S. F. Kerstan, T. Ortin and F. Riccioni, IIB nine-branes, hep-th/0601128.
40. 9 levels: a first algorithmic approach, J. High Energy Phys. 0508, 012 (2005) [hep-th/0504230].
41. C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438, 109-137 (1995) [hep-th/9410167].
42. E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443, 85-126 (1995) [hep-th/9503124].
43. C. Hillman, A. Kleinschmidt and H. Nicolai, A note on gauge fixing in supergravity/Kac-Moody correspondences, hep-th/0603156.
44. 10), Supergravity and Fermions, J. High Energy Phys. 0608, 046 (2006) [hep-th/0606105].
45. L. J. Romans, Massive N = 2a supergravity in ten dimensions, Phys. Lett. B 169, 374-380 (1986).
46. J. Maharana and J. H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B 390, 3-32 (1993) [hep-th/9207016].
47. E. Bergshoeff, M. de Roo, M. B. Green, G. Papadopoulos and P. K. Townsend, Duality of type II 7-branes and 8-branes, Nucl. Phys. B 470, 113 (1996) [hep-th/9601150].
48. J. H. Schwarz and P. C. West, Symmetries and transformations of chiral N = 2, D =10 supergravity, Phys. Lett. B 126, 301 (1983).
49. J. H. Schwarz, Covariant field equations of chiral N = 2, D = 10 supergravity, Nucl. Phys. B 226, 269 (1983).
50. J. H. Schwarz, An SL(2, ℤ) multiplet of type IIB superstrings, Phys. Lett. B 360, 13 (1995) [Erratum-ibid. B364, 252 (1995)] [hep-th/9508143].
51. J. Polchinski, Dirichlet-branes and Ramond-Ramond charges, Phys. Rev. Lett. 75, 4724 (1995) [hep-th/9510017].
52. A. V. Razumov and M. V. Saveliev, Lie Algebras, Geometry and Toda-Type Systems, Cambridge Lecture Notes in Physics (Cambridge University Press, 1997).
53. O. Babelon, D. Bernard and M. Talon, Introduction to Classical Integrable Systems (Cambridge University Press, 2003).
54. 10 cosmology, J. High Energy Phys. 0601, 137 (2006) [hep-th/0511290].
55. N. Ohta, Accelerating cosmologies from S-branes, Phys. Rev. Lett. 91, 061303 (2003) [hep-th/0303238].
56. M. N. R. Wohlfarth, Accelerating cosmologies and a phase transition in M-theory, Phys. Lett. B 563, 1 (2003) [hep-th/0304089].
57. N. Ohta, Accelerating cosmologies and inflation from M/superstring theories, Int. J. Mod. Phys. A 20 (2005) [hep-th/0411230].
58. F. Englert, L. Houart, A. Taormina and P. C. West, The symmetry of M-theories, J. High Energy Phys. 0309, 020 (2003) [hep-th/0304206].
59. F. Englert, L. Houart and P. C. West, Intersection rules, dynamics and symmetries, J. High Energy Phys. 0308, 025 (2003) [hep-th/0307024].
60. 11 origin, hep-th/0402140.
61. +++ invariant formulation of gravity and M-theories: exact intersecting brane solutions, J. High Energy Phys. 0405, 059 (2004) [hep-th/0405082].
62. +++ and brane solutions, hep-th/0405149.
63. L. Houart, Kac-Moody algebras in gravity and M-theories, hep-th/0511009.
64. T. Damour, A. Kleinschmidt and H. Nicolai, Hidden symmetries and the fermionic sector of eleven-dimensional supergravity, hep-th/0512163.
65. 8 invariance of 11-dimensional supergravity, hep-th/0512292.
66. S. de Buyl, M. Henneaux and L. Paulot, Hidden symmetries and Dirac fermions, Class. Quant. Grav. 22, 3595 (2005) [hep-th/0506009].
67. M. J. Duff and K. S. Stelle, Multimembrane solutions of D = 11 supergravity, Phys. Lett. B 253, 113-118 (1991).
68. M. J. Duff and J. T. Liu, Hidden space-time symmetries and generalized holonomy in M-theory, Nucl. Phys. B 674, 217-230 (2003) [hep-th/0303140].
69. C. Hull, Holonomy and symmetry in M-theory, hep-th/0305039.
70. A. Keurentjes, The topology of U Duality (sub)groups, Class. Quant. Grav. 21, 1695-1708 (2004) [hep-th/0309106].
71. O. Bärwald and P. C. West, Brane rotating symmetries and the five-brane equations of motion, Phys. Lett. B 476, 157-164 (2000) [hep-th/9912226].
72. 10), Phys. Lett. B 637, 107-112 (2006) [hep-th/0603205].
73. P. Breitenlohner and D. Maison, On the Geroch group, Ann. Poincaré Phys. Theor. 46, 215-246 (1987).
74. H, hep-th/0512092.
75. 10, hep-th/0608092.