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Hidden Symmetries of M-Theory and Its Dynamical Realization
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss hidden symmetries of M-theory, its feedback on the construction of the M-theory effective action, and a response of the effective action when locality is preserved. In particular, the locality of special symmetries of the duality-symmetric linearized gravity constraints the index structure of the dual to graviton field in the same manner as it is required to separate the levels 0 and 1 generators subalgebra from the infinite-dimensional hidden symmetry algebra of gravitational theory. This conclusion fails once matter fields are taken into account and we give arguments for that. We end up outlining current problems and development perspectives.
Keywords: duality; gravity; supergravity. 
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Alexei J. Nurmagambetov. Hidden Symmetries of M-Theory and Its Dynamical Realization. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a21/

[1] West P. C., “$E_{11}$ and M-theory”, Classical Quantum Gravity, 18 (2001), 4443–4460 ; hep-th/0104081 | DOI | MR | Zbl

[2] Gaberdiel M. R., Olive D. I., West P. C., “A class of Lorentzian Kac–Moody algebras”, Nuclear Phys. B, 645 (2002), 403–437 ; hep-th/0205068 | DOI | MR | Zbl

[3] Buyl S., Kac–Moody algebras in M-theory, , and references therein hep-th/0608161

[4] West P. C., “Very extended $E_8$ and $A_8$ at low levels, gravity and supergravity”, Classical Quantum Gravity, 20 (2002), 2393–2406 ; hep-th/0212291 | DOI

[5] Bandos I., Lechner K., Nurmagambetov A., Pasti P., Sorokin D., Tonin M., “Covariant action for super-five-brane of M theory”, Phys. Rev. Lett., 78 (1997), 4332–4335 ; hep-th/9701149 | DOI | MR

[6] Aganagic M., Park J., Popescu C., Schwarz J. H., “World-volume action of the M theory five-brane”, Nuclear Phys. B, 496 (1997), 191–214 ; hep-th/9701166 | DOI | MR | Zbl

[7] Bandos I., Berkovits N., Sorokin D., “Duality-symmetric eleven-dimensional supergravity and its coupling to M-branes”, Nuclear Phys. B, 522 (1998), 214–233 ; hep-th/9711055 | DOI | MR | Zbl

[8] Pasti P., Sorokin D., Tonin M., “Note on manifest Lorentz and general coordinate invariance in duality symmetric models”, Phys. Lett. B, 352 (1995), 59–63 ; ; Pasti P., Sorokin D., Tonin M., “Duality symmetric actions with manifest space-time symmetries”, Phys. Rev. D, 52 (1995), 4277–4281 ; ; Pasti P., Sorokin D., Tonin M., “On Lorentz invariant actions for chiral $p$-forms”, Phys. Rev. D, 55 (1997), 6292–6298 ; hep-th/9503182hep-th/9506109hep-th/9611100 | DOI | DOI | MR | DOI | MR

[9] Damour T., Henneaux M., Nicolai H., “$E_{10}$ and a “small tension expansion” of M-theory”, Phys. Rev. Lett., 89 (2002), 221601, 4 pp., ages ; hep-th/0207267 | DOI | MR

[10] Englert F., Houart L., “$\mathcal G^{+++}$ invariant formulation of gravity and M-theories: exact BPS solutions”, J. High Energy Phys., 2004:1 (2004), 002, 45 pp., ages ; hep-th/0311255 | DOI | MR

[11] Henneaux M., Persson D., Spindel Ph., Spacelike singularities and hidden symmetries of gravity, arXiv:0710.1818

[12] Damour T., Nicolai H., Symmetries, singularities and the de-emergence of space, arXiv:0705.2643 | MR

[13] Bandos I. A., Nurmagambetov A. J., Sorokin D. P., “Various faces of type IIA supergravity”, Nuclear Phys. B, 676 (2004), 189–228 ; hep-th/0307153 | DOI | MR | Zbl

[14] Cremmer E., Julia B., Lü H., Pope C. N., “Dualisation of dualities II: Twisted self-duality of doubled fields and superdualities”, Nuclear Phys. B, 535 (1998), 242–292 ; hep-th/9806106 | DOI | MR | Zbl

[15] Nurmagambetov A. J., “The sigma-model representation for the duality-symmetric $\mathrm D=11$ supergravity”, Proceedings of Fifth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 23–29, 2003, Kyiv), Proceedings of Institute of Mathematics, 50, no. 2, eds. A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko, Kyiv, 2004, 894–901 ; hep-th/0312157 | MR | Zbl

[16] Nurmagambetov A. J., “Sigma-model-like action for type IIA supergravity in doubled field approach”, Proceedings of International Workshop SQS'03 (July 24–29, 2003, Dubna), 2003, 84–89

[17] Nurmagambetov A. J., “On the sigma-model structure of type IIA supergravity action in doubled field approach”, JETP Lett., 79 (2004), 191–195 ; hep-th/0403100 | DOI

[18] Nurmagambetov A.J., “Duality-symmetric gravity and supergravity: testing the PST approach”, Ukr. J. Phys., 51 (2006), 330–338 ; hep-th/0407116 | MR

[19] Nurmagambetov A. J., “Duality-symmetric approach to General Relativity and supergravity”, SIGMA, 2 (2006), 020, 34 pp., ages ; hep-th/0602145 | MR | Zbl

[20] Morrison D. R., TASI lectures on compactification and duality, hep-th/0411120 | MR

[21] Nurmagambetov A. J., “On $E(11)$ of M-theory: 1. Hidden symmetries of maximal supergravities and LEGO of Dynkin diagrams”, Proceedings of II International Conference on QED and Statistical Physics (September 19–23, Kharkov, Ukraine), Problems of Atomic Science and Technology, 3, 2007, 51–55

[22] Lambert N. D., West P. C., “Coset symmetries in dimensionally reduced bosonic string theory”, Nuclear Phys. B, 615 (2001), 117–132 ; hep-th/0107209 | DOI | MR | Zbl

[23] Nurmagambetov A. J., “Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity”, JETP Lett., 79 (2004), 355–359 ; hep-th/0403101 | DOI

[24] Kac V. G., Infinite dimensional Lie algebras, Birkhäuser, Boston, 1983 | MR | Zbl

[25] Bergshoeff E., Nutma T. A., De Baetselier I., $E_{11}$ and the embedding tensor, arXiv:0705.1304

[26] Kleinschmidt A., Schnakenburg I., West P. C., “Very-extended Kac–Moody algebras and their interpretation at low levels”, Classical Quantum Gravity, 21 (2004), 2493–2525 ; hep-th/0309198 | DOI | MR | Zbl

[27] Nicolai H., Townsend P. K., Nieuwenhuizen P., “Comments on 11-dimensional supergravity”, Lett. Nuovo Cimento, 30 (1981), 315–320 | DOI | MR

[28] D'Auria R., Fre P., “Geometric supergravity in $d=11$ and its hidden supergroup”, Nuclear Phys. B, 201 (1982), 101–140 | DOI | MR

[29] Ehlers J., Les théories relativistes de la gravitation, CNRS, Paris, 1959

[30] Matzner R., Misner C., “Gravitational field equations for sources with axial symmetry and angular momentum”, Phys. Rev., 154 (1967), 1229–1232 | DOI

[31] Geroch R., “A method for generating solutions of Einstein's equations”, J. Math. Phys., 12 (1971), 918–924 | DOI | MR | Zbl

[32] Breitenlohner P., Maison D., “On the Geroch group”, Ann. Inst. H. Poincaré, 46 (1987), 215–246 | MR | Zbl

[33] Julia B., Kac–Moody symmetry of gravitation and supergravity theories, Preprint LPTENS-82-22, 1982, AMS-SIAM Seminar Proceedings, Chicago, 1982, 25 pp., ages | MR

[34] Nicolai H., “A hyperbolic Lie algebra from supergravity”, Phys. Lett. B, 276 (1992), 333–340 | DOI | MR

[35] van Nieuwenhuizen P., “Supergravity”, Phys. Rep., 68 (1981), 189–398 | DOI | MR

[36] Garcia-Compean H., Obregon O., Plebansky J. F., Ramirez C., “Towards a gravitational analogue to $S$-duality in non-Abelian gauge theories”, Phys. Rev. D, 57 (1998), 7501–7506 ; hep-th/9711115 | DOI | MR

[37] Garcia-Compean H., Obregon O., Ramirez C., “Gravitational duality in MacDowell–Mansouri gauge theory”, Phys. Rev. D, 58 (1998), 104012, 3 pp., ages ; hep-th/9802063 | DOI | MR

[38] Nieto J. A., “$S$-duality for linearized gravity”, Phys. Lett. A, 262 (1999), 274–281 ; hep-th/9910049 | DOI | MR | Zbl

[39] Hull C. M., “Gravitational duality, branes and charges”, Nuclear Phys. B, 509 (1998), 216–251 ; hep-th/9705162 | DOI | MR | Zbl

[40] Hull C. M., “Strongly coupled gravity and duality”, Nuclear Phys. B, 583 (2000), 237–259 ; hep-th/0004195 | DOI | MR | Zbl

[41] Hull C. M., “Duality in gravity and higher spin gauge fields”, J. High Energy Phys., 2001:9 (2001), 027, 25 pp., ages ; hep-th/0107149 | DOI | MR

[42] Boulanger N., Cnockaert S., Henneaux M., “A note on spin-s duality”, J. High Energy Phys., 2003:6 (2003), 060, 18 pp., ages ; hep-th/0306023 | DOI | MR

[43] Henneaux M., Teitelboim C., “Duality in linearized gravity”, Phys. Rev. D, 71 (2005), 024018, 8 pp., ages ; gr-qc/0408101 | DOI | MR

[44] Julia B., Levie J., Ray S., “Gravitational duality near de Sitter space”, J. High Energy Phys., 2005:11 (2005), 025, 13 pp., ages ; hep-th/0507262 | DOI | MR

[45] Ajith K. M., Harikumar E., Sivakumar M., “Dual linearized gravity in arbitrary dimensions”, Classical Quantum Gravity, 22 (2005), 5385–5396 ; hep-th/0411202 | DOI | MR

[46] Padmanabhan T., From graviton to gravity: myths and reality, gr-qc/0409089 | MR

[47] Leclerc M., “Canonical and gravitational stress-energy tensors”, Internat. J. Modern Phys. D, 15 (2006), 959–990 ; gr-qc/0510044 | DOI | MR