Geometric configurations, regular subalgebras of E10 and M-theory cosmology

Journal of High Energy Physics

Volumn 2006, Issue 10, 2006, Pages

  Henneaux, Marc ^a,b   Leston, Mauricio ^a,c   Persson, Daniel ^a   Spindel, Philippe ^d  

^a INTERNATIONAL SOLVAY INSTITUTES   (Belgium)

^b CENTRO DE ESTUDIOS CIENTÍFICOS CECS   (Chile)

^c INSTITUTO DE ASTRONOMÍA Y FÍSICA DEL ESPACIO   (Argentina)

^d UNIVERSITY OF MONS   (Belgium)

Author keywords

Global Symmetries; M Theory; String Duality

Indexed keywords

EID: 33846151089     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/10/021     Document Type: Review

References (46)

1. J. Demaret, J.L. Hanquin, M. Henneaux and P. Spindel, Cosmological models in eleven-dimensional supergravity 1985 Nucl. Phys. B 252 538
2. T. Damour and M. Henneaux, Oscillatory behaviour in homogeneous string cosmology models 2000 Phys. Lett. B 488 108 [hep-th/0006171]
3. 10 and arithmetical chaos in superstring cosmology, 2001 Phys. Rev. Lett. 86 4749 [hep-th/0012172]
4. V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, Oscillatory approach to a singular point in the relativistic cosmology 1970 Adv. Phys. 19 525-573
5. D. M. Chitre, Ph.D thesis, University of Maryland
6. C.W. Misner, The mixmaster cosmological metrics [gr-qc/9405068]
7. A. A. Kirillov, 1993 Sov. Phys. JETP 76 355
8. A.A. Kirillov and V.N. Melnikov, Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology 1995 Phys. Rev. D 52 723 [gr-qc/9408004]
9. V.D. Ivashchuk, A.A. Kirillov and V.N. Melnikov, Stochastic behavior of multidimensional cosmological models near a singularity 2000 Russ. Phys. J. 37 (1994) 1102
10. V.D. Ivashchuk, A.A. Kirillov and V.N. Melnikov, Stochastic properties of multidimensional cosmological models near a singular point JETP Lett. 60 (1994) 235 [Pisma Zh. Eksp. Teor. Fiz. 60 (1994) 225]
11. V.D. Ivashchuk and V.N. Melnikov, Billiard representation for multidimensional cosmology with intersecting p-branes near the singularity J. Math. Phys. 41 6341 [hep-th/9904077]
12. T. Damour, M. Henneaux and H. Nicolai, Cosmological billiards 2003 Class. Quantum Grav. 20 R145 [hep-th/0212256]
13. T. Damour, M. Henneaux, B. Julia and H. Nicolai, Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models 2001 Phys. Lett. B 509 323 [hep-th/0103094]
14. 10 and a 'small tension expansion' of M-theory, 2002 Phys. Rev. Lett. 89 221601 [hep-th/0207267]
15. B. Julia, Kac-Moody symmetry of gravitation and supergravity theories LPTENS 82/22, invited talk given at AMS-SIAM Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, Chicago, Ill., Jul 6-16, 1982
16. 11 and M-theory, 2001 Class. Quantum Grav. 18 4443 [hep-th/0104081]
17. V.D. Ivashchuk, V.N. Melnikov and D. Singleton, On avoiding cosmological oscillating behavior for s-brane solutions with diagonal metrics 2005 Phys. Rev. D 72 103511 [gr-qc/0509065]
18. 10, K. Academie der Wissenschaften, Vienna, Sitzungsbereichte der matematisch naturewissenshaftlichen classe, 84 II (1881) 1291-1314
19. D. Hilbert and S. Cohn-Vossen, Geometry and the imagination
20. W. Page and H. L. Dorwart, Numerical patterns and geometrical configurations 1984 Mathematics Magazine 57 no. 2, 82-92
21. V. Kac, Infinite dimensional Lie algebras 3rd Ed., (Cambridge University Press), 1990
22. M. Henneaux and B. Julia, Hyperbolic billiards of pure D = 4 supergravities 2003 J. High Energy Phys. JHEP05(2003)047 [hep-th/0304233]
23. S. R. Coleman, J. Wess and B. Zumino, Structure of phenomenological lagrangians, 1 1969 Phys. Rev. 177 2239
24. C. G.. Callan, S. R. Coleman, J. Wess and B. Zumino, Structure of phenomenological lagrangians 1969 Phys. Rev. 177 2247
25. 10, in: Differential geometric methods in theoretical physics NATO Advanced research Workshop, K. Bleuler and M. Werner eds., Kluwer, 1988
26. 11, [hep-th/0301017]
27. 9 levels, [hep-th/0410245]
28. M.R. Gaberdiel, D.I. Olive and P.C. West, A class of lorentzian Kac-Moody algebras 2002 Nucl. Phys. B 645 403 [hep-th/0205068]
29. E.B. Dynkin, Semisimple subalgebras of semisimple Lie algebras American Mathematical Society Translations Series 2, Vol 6 (1957) 111
30. 10 and SO(9,9) invariant supergravity, 2004 J. High Energy Phys. JHEP07(2004)041 [hep-th/0407101]
31. 10 orbifolds, 2005 J. High Energy Phys. JHEP06(2005)057 [hep-th/0409037]
32. A.J. Feingold and H. Nicolai, Subalgebras of hyperbolic Kac-Moody algebras [math.qa/0303179]
33. F. Englert, M. Henneaux and L. Houart, From very-extended to overextended gravity and M-theories 2005 J. High Energy Phys. JHEP02(2005)070 [hep-th/0412184]
34. P. Fre et al., Cosmological backgrounds of superstring theory and solvable algebras: oxidation and branes 2004 Nucl. Phys. B 685 3 [hep-th/0309237]
35. 8(8) subalgebras and p-branes, 2004 Nucl. Phys. B 694 239 [hep-th/0312189]
36. 10 cosmology, 2006 J. High Energy Phys. JHEP01(2006)137 [hep-th/0511290]
37. J. Baez, The octonions 2001 [math.ra/0105155]
38. R.D. Schafer, An introduction to non-associative algebras (Academic Press), New York, 1966
39. J. Bokowski and B. Sturmfels, Computational synthetic geometry, Lecture Notes in Mathematics 1355 (Springer-Verlag, Berlin) Heidelberg, 1989
40. M. Gutperle and A. Strominger, Spacelike branes 2002 J. High Energy Phys. JHEP04(2002)018 [hep-th/0202210]
41. F. Englert and L. Houart, G+++ invariant formulation of gravity and M-theories: exact intersecting brane solutions 2004 J. High Energy Phys. JHEP05(2004)059 [hep-th/0405082]
42. F. Englert and L. Houart, G+++ invariant formulation of gravity and M-theories: exact BPS solutions 2004 J. High Energy Phys. JHEP01(2004)002 [hep-th/0311255]
43. N. Ohta, Intersection rules for S-branes 2003 Phys. Lett. B 558 213 [hep-th/0301095]
44. R. Argurio, F. Englert and L. Houart, Intersection rules for p-branes 1997 Phys. Lett. B 398 61 [hep-th/9701042]
45. N. Ohta, Intersection rules for non-extreme p-branes 1997 Phys. Lett. B 403 218 [hep-th/9702164]
46. S. de Buyl, G. Pinardi and C. Schomblond, Einstein billiards and spatially homogeneous cosmological models 2003 Class. Quantum Grav. 20 5141 [hep-th/0306280]