Abstract
We classify the enhanced helicity symmetry of the Ehlers group to extended supergravity theories in any dimension. The vanishing character of the pseudo-Riemannian cosets occurring in this analysis is explained in terms of Poincaré duality .The latter resides in the nature of regularly embedded quotient subgroups which are noncompact rank preserving.
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References
M. Goroff and J.H. Schwarz, D-dimensional gravity in the light cone gauge, Phys. Lett. B 127 (1983) 61 [INSPIRE].
E. Cremmer and B. Julia, The N = 8 Supergravity Theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48 [INSPIRE].
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
C. Hull and P. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C. Pope, Higher dimensional origin of D = 3 coset symmetries, hep-th/9909099 [INSPIRE].
H. Lü and C. Pope, P-brane solitons in maximal supergravities, Nucl. Phys. B 465 (1996) 127 [hep-th/9512012] [INSPIRE].
N. Marcus and J.H. Schwarz, Three-Dimensional Supergravity Theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].
E. Cremmer, Supergravities in 5 Dimensions, in Superspace and Supergravity, S.W. Hawking and M. Rocek eds., Cambridge University Press, Cambridge, U.K. (1981).
B. Julia, Group Disintegrations, in Superspace and Supergravity, S.W. Hawking and M. Rocek eds., Cambridge University Press, Cambridge, U.K. (1981).
S. Ananth, L. Brink and P. Ramond, Eleven-dimensional supergravity in light-cone superspace, JHEP 05 (2005) 003 [hep-th/0501079] [INSPIRE].
L. Brink, S.-S. Kim and P. Ramond, E 8(8) in Light Cone Superspace, JHEP 07 (2008) 113 [arXiv:0804.4300] [INSPIRE].
L. Brink, S.-S. Kim and P. Ramond, E 7(7) on the Light Cone, JHEP 06 (2008) 034 [arXiv:0801.2993] [INSPIRE].
B. de Wit, A. Tollsten and H. Nicolai, Locally supersymmetric D = 3 nonlinear σ-models, Nucl. Phys. B 392 (1993) 3 [hep-th/9208074] [INSPIRE].
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, U.S.A. (1978).
R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications, Dover Publications (2006).
A. Keurentjes, The Group theory of oxidation, Nucl. Phys. B 658 (2003) 303 [hep-th/0210178] [INSPIRE].
A. Keurentjes, The Group theory of oxidation 2: Cosets of nonsplit groups, Nucl. Phys. B 658 (2003) 348 [hep-th/0212024] [INSPIRE].
N. Marcus, A. Sagnotti and J.H. Schwarz, Infinite symmetry algebras of extended supergravity theories, Nucl. Phys. B 243 (1984) 335 [INSPIRE].
M. Günaydin, G. Sierra and P. Townsend, Exceptional Supergravity Theories and the MAGIC Square, Phys. Lett. B 133 (1983) 72 [INSPIRE].
M. Günaydin, G. Sierra and P. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].
M. Günaydin, Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace, arXiv:0908.0374 [INSPIRE].
P. Truini, Exceptional Lie Algebras, SU(3) and Jordan Pairs, arXiv:1112.1258 [INSPIRE].
W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
M. Bertolini and M. Trigiante, Regular RR and NS-NS BPS black holes, Int. J. Mod. Phys. A 15 (2000) 5017 [hep-th/9910237] [INSPIRE].
R. D’Auria, S. Ferrara, M. Lledó and V. Varadarajan, Spinor algebras, J. Geom. Phys. 40 (2001) 101 [hep-th/0010124] [INSPIRE].
S. Ferrara, C.A. Savoy and B. Zumino, General massive multiplets in extended supersymmetry, Phys. Lett. B 100 (1981) 393 [INSPIRE].
G. Compere, S. de Buyl, E. Jamsin and A. Virmani, G 2 Dualities in D = 5 Supergravity and Black Strings, Class. Quant. Grav. 26 (2009) 125016 [arXiv:0903.1645] [INSPIRE].
E. Bergshoeff, W. Chemissany, A. Ploegh, M. Trigiante and T. Van Riet, Generating Geodesic Flows and Supergravity Solutions, Nucl. Phys. B 812 (2009) 343 [arXiv:0806.2310] [INSPIRE].
L. Borsten, M.J. Duff, S. Ferrara, A. Marrani and W. Rubens, Small Orbits, Phys. Rev. D 85 (2012) 086002 [arXiv:1108.0424] [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Geometry of Type II Superstrings and the Moduli of Superconformal Field Theories, Int. J. Mod. Phys. A 4 (1989) 2475 [INSPIRE].
E. Cremmer and A. Van Proeyen, Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings, Class. Quant. Grav. 2 (1985) 445 [INSPIRE].
J. Luciani, Coupling of O(2) Supergravity with Several Vector Multiplets, Nucl. Phys. B 132 (1978) 325 [INSPIRE].
J. Bagger and E. Witten, Matter Couplings in N = 2 Supergravity, Nucl. Phys. B 222 (1983) 1 [INSPIRE].
A. Salam and E. Sezgin, Anomaly freedom in chiral supergravities, Phys. Scripta 32 (1985) 283.
S. Randjbar-Daemi, A. Salam, E. Sezgin and J. Strathdee, An Anomaly Free Model in Six-Dimensions, Phys. Lett. B 151 (1985) 351 [INSPIRE].
S. Ferrara, F. Riccioni and A. Sagnotti, Tensor and vector multiplets in six-dimensional supergravity, Nucl. Phys. B 519 (1998) 115 [hep-th/9711059] [INSPIRE].
F. Riccioni and A. Sagnotti, Consistent and covariant anomalies in six-dimensional supergravity, Phys. Lett. B 436 (1998) 298 [hep-th/9806129] [INSPIRE].
H. Nishino and E. Sezgin, New couplings of six-dimensional supergravity, Nucl. Phys. B 505 (1997) 497 [hep-th/9703075] [INSPIRE].
M. Günaydin, H. Samtleben and E. Sezgin, On the Magical Supergravities in Six Dimensions, Nucl. Phys. B 848 (2011) 62 [arXiv:1012.1818] [INSPIRE].
D.V. Alekseevskii, Classification of quaternionic spaces with a transitive solvable group of motions, Math. USSR Izvestija 9 (1975) 297.
E.B. Dynkin, Semisimple Subalgebras of Semisimple Lie Algebras, American Mathematical Society Translations, Series 2 6 (1957) 111.
E.B. Dynkin, The Maximal Subgroups of the Classical Groups, American Mathematical Society Translations, Series 2 6 (1957) 245.
A. Minchenko, The Semisimple Subalgebras of Exceptional Lie Algebras, Trans. Moscow Math. Soc. 67 (2006) 225.
H. Lü, C. Pope and K. Stelle, Weyl group invariance and p-brane multiplets, Nucl. Phys. B 476 (1996) 89 [hep-th/9602140] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fré and M. Trigiante, RR scalars, U duality and solvable Lie algebras, Nucl. Phys. B 496 (1997) 617 [hep-th/9611014] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fré, R. Minasian and M. Trigiante, Solvable Lie algebras in type IIA, type IIB and M theories, Nucl. Phys. B 493 (1997) 249 [hep-th/9612202] [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C. Pope, Dualization of dualities. 1., Nucl. Phys. B 523 (1998) 73 [hep-th/9710119] [INSPIRE].
A. Kleinschmidt and H. Nicolai, E 10 and SO(9,9) invariant supergravity, JHEP 07 (2004) 041 [hep-th/0407101] [INSPIRE].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, IIA ten-forms and the gauge algebras of maximal supergravity theories, JHEP 07 (2006) 018 [hep-th/0602280] [INSPIRE].
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ArXiv ePrint: 1206.1255
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Ferrara, S., Marrani, A. & Trigiante, M. Super-Ehlers in any dimension. J. High Energ. Phys. 2012, 68 (2012). https://doi.org/10.1007/JHEP11(2012)068
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DOI: https://doi.org/10.1007/JHEP11(2012)068