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The linearized Einstein equations in D spacetime dimensions can be written as twisted self-duality equations expressing that the linearized curvature tensor of the graviton described by a rank-two symmetric tensor, is dual to the linearized curvature tensor of the "dual graviton" described by a tensor of (D-3,1) Young symmetry type.
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The cohomological theorems underlying these results go back to P.J. Olver, “Differential Hyperforms”, University of Minnesota, Mathematics Report 82-101 (1982) and have been analyzed in the present context of field theories with tensor fields of mixed symmetry type in [ 22 ] and [ 23 ]
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Actions which contain additional fields and additional gauge symmetries and which are manifestly duality and Lorentz invariant have been proposed in P. Pasti, D. P. Sorokin and M. Tonin, “Note on manifest Lorentz and general coordinate invariance in duality symmetric models,” Phys. Lett. B 352
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B. Julia, J. Levie and S. Ray, “Gravitational duality near de Sitter space,” JHEP 0511
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C. M. Hull, “Duality in gravity and higher spin gauge fields,” JHEP 0109
2001
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T. Damour, M. Henneaux and H. Nicolai, “E(10) and a ’small tension expansion’ of M theory,” Phys. Rev. Lett. 89
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M. Henneaux and C. Teitelboim, “Duality in linearized gravity,” Phys. Rev. D 71
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The literature on duality is huge. We have mentioned here only the works that recognize it as a bone fide symmetry of the action (and not just of the equations of motion) since off-shell duality is the central feature investigated in this article
Cited in the paper.
C. Bunster and M. Henneaux, “The Action for Twisted Self-Duality,” Phys. Rev. D 83
2011
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2012
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2012
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R. Kallosh, “ E 7 ( 7 ) E_{7(7)} Symmetry and Finiteness of N=8 Supergravity,” JHEP 1203
2012
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