Abstract
We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds.
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J. Figueroa-O’Farrill and G. Papadopoulos, Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities, JHEP 03 (2003) 048 [hep-th/0211089] [SPIRES].
J. Figueroa-O’Farrill and G. Papadopoulos, Plücker-type relations for orthogonal planes, math.AG/0211170.
J.P. Gauntlett and S. Pakis, The geometry of D = 11 Killing spinors, JHEP 04 (2003) 039 [hep-th/0212008] [SPIRES].
J.P. Gauntlett, J.B. Gutowski and S. Pakis, The geometry of D = 11 null Killing spinors, JHEP 12 (2003) 049 [hep-th/0311112] [SPIRES].
J. Gillard, U. Gran, G. Papadopoulos, The spinorial geometry of supersymmetric backgrounds, Class. and Quant. Grav. 22 (2005) 1033] [hep-th/0410155] [SPIRES].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, N = 31 is not IIB, JHEP 02 (2007) 044 [hep-th/0606049] [SPIRES].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, N = 31, D = 11, JHEP 02 (2007) 043 [hep-th/0610331] [SPIRES].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, IIB solutions with N > 28 Killing spinors are maximally supersymmetric, JHEP 12 (2007) 070 [arXiv:0710.1829] [SPIRES].
I. Bena and R. Roiban, Supergravity pp-wave solutions with 28 and 24 supercharges, Phys. Rev. D 67 (2003) 125014 [hep-th/0206195] [SPIRES].
U. Gran, J. Gutowski and G. Papadopoulos, Classification of IIB backgrounds with 28 supersymmetries, JHEP 01 (2010) 044 [arXiv:0902.3642] [SPIRES].
J.M. Figueroa-O’Farrill and S. Gadhia, M-theory preons cannot arise by quotients, JHEP 06 (2007) 043 [hep-th/0702055] [SPIRES].
I.A. Bandos, J.A. de Azcarraga and O. Varela, On the absence of BPS preonic solutions in IIA and IIB supergravities, JHEP 09 (2006) 009 [hep-th/0607060] [SPIRES].
M.J. Duff, M-theory on manifolds of G 2 holonomy: the first twenty years, hep-th/0201062 [SPIRES].
J.M. Figueroa-O’Farrill, P. Meessen and S. Philip, Supersymmetry and homogeneity of M-theory backgrounds, Class. Quant. Grav. 22 (2005) 207 [hep-th/0409170] [SPIRES].
J.M. Figueroa-O’Farrill, The homogeneity conjecture for supergravity backgrounds, J. Phys. Conf. Ser. 175 (2009) 012002 [arXiv:0812.1258] [SPIRES].
P.K. Townsend, M-theory from its superalgebra, hep-th/9712004 [SPIRES].
I.A. Bandos, J.A. de Azcarraga, J.M. Izquierdo and J. Lukierski, BPS states in M-theory and twistorial constituents, Phys. Rev. Lett. 86 (2001) 4451 [hep-th/0101113] [SPIRES].
C. Hull, Holonomy and symmetry in M-theory, hep-th/0305039 [SPIRES].
M.J. Duff and J.T. Liu, Hidden spacetime symmetries and generalized holonomy in M-theory, Nucl. Phys. B 674 (2003) 217 [hep-th/0303140] [SPIRES].
G. Papadopoulos and D. Tsimpis, The holonomy of the supercovariant connection and Killing spinors, JHEP 07 (2003) 018 [hep-th/0306117] [SPIRES].
G. Papadopoulos and D. Tsimpis, The holonomy of IIB supercovariant connection, Class. Quant. Grav. 20 (2003) L253 [hep-th/0307127] [SPIRES].
J.M. Figueroa-O’Farrill and J. Simon, Supersymmetric Kaluza-Klein reductions of AdS backgrounds, Adv. Theor. Math. Phys. 8 (2004) 217 [hep-th/0401206] [SPIRES].
J.M. Figueroa-O’Farrill, O. Madden, S.F. Ross and J. Simon, Quotients of AdS(p+1) x S**q: causally well-behaved spaces and black holes, Phys. Rev. D 69 (2004) 124026 [hep-th/0402094] [SPIRES].
S. Fernando, M. Gunaydin and S. Hyun, Oscillator construction of spectra of PP-wave superalgebras in eleven dimensions, Nucl. Phys. B 727 (2005) 421 [hep-th/0411281] [SPIRES].
J.P. Gauntlett and C.M. Hull, pp-waves in 11-dimensions with extra supersymmetry, JHEP 06 (2002) 013 [hep-th/0203255] [SPIRES].
J.M. Figueroa-O’Farrill and G. Papadopoulos, Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory, JHEP 08 (2001) 036 [hep-th/0105308] [SPIRES].
M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A new maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [SPIRES].
E. Cremmer, B. Julia and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76 (1978) 409 [SPIRES].
U. Gran, G. Papadopoulos and D. Roest, Systematics of M-theory spinorial geometry, Class. Quant. Grav. 22 (2005) 2701 [hep-th/0503046] [SPIRES].
P. De Medeiros, J.M. Figueroa-O’Farrill and E. Mendez-Escobar, Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space, JHEP 07 (2008) 111 [arXiv:0805.4363] [SPIRES].
P.G.O. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett. B 97 (1980) 233 [SPIRES].
J. Kowalski-Glikman, Vacuum states in supersymmetric Kaluza-Klein theory, Phys. Lett. B 134 (1984) 194 [SPIRES].
J. Michelson, A pp-wave with 26 supercharges, Class. Quant. Grav. 19 (2002) 5935 [hep-th/0206204] [SPIRES].
U. Gran, G. Papadopoulos, D. Roest and P. Sloane, Geometry of all supersymmetric type-I backgrounds, JHEP 08 (2007) 074 [hep-th/0703143] [SPIRES].
U. Gran, J. Gutowski and G. Papadopoulos, Invariant Killing spinors in 11D and type-II supergravities, Class. Quant. Grav. 26 (2009) 155004 [arXiv:0802.2040] [SPIRES].
P.A. Nagy, Prolongations of Lie algebras and applications, arXiv:0712.1398.
G. Papadopoulos, M2-branes, 3-Lie algebras and Plücker relations, JHEP 05 (2008) 054 [arXiv:0804.2662] [SPIRES].
G. Papadopoulos, On the structure of k-Lie algebras, Class. Quant. Grav. 25 (2008) 142002 [arXiv:0804.3567] [SPIRES].
J.P. Gauntlett and J.B. Gutowski, Constraining maximally supersymmetric membrane actions, JHEP 06 (2008) 053 [arXiv:0804.3078] [SPIRES].
M. Cvetic, H. Lu and C.N. Pope, M-theory pp-waves, Penrose limits and supernumerary supersymmetries, Nucl. Phys. B 644 (2002) 65 [hep-th/0203229] [SPIRES].
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Gran, U., Gutowski, J. & Papadopoulos, G. M-theory backgrounds with 30 Killing spinors are maximally supersymmetric. J. High Energ. Phys. 2010, 112 (2010). https://doi.org/10.1007/JHEP03(2010)112
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DOI: https://doi.org/10.1007/JHEP03(2010)112