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We generalize Cremmer-Julia 1st order action of $N=8$ supergravity with manifest $E_{7(7)}$ symmetry to cases of $N=6$ with manifest $SO^*(12)$ and $N=5$ with manifest $SU(1,5)$ duality symmetries.
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R. Kallosh and M. Soroush, Explicit Action of E(7)(7) on N=8 Supergravity Fields , Nucl. Phys. B801
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R. Kallosh, E 7 ( 7 ) E_{7(7)} Symmetry and Finiteness of N=8 Supergravity , JHEP 03
2012
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2012
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W. Chemissany, R. Kallosh and T. Ortin, Born-Infeld with Higher Derivatives , Phys. Rev. D85
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R. Kallosh and T. Ortin, New E 7 ( 7 ) E_{7(7)} invariants and amplitudes , JHEP 09
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C. Hillmann, E(7)(7) invariant Lagrangian of d=4 N=8 supergravity , JHEP 04
2010
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S. Ferrara and R. Kallosh, Creation of Matter in the Universe and Groups of Type E7 , JHEP 12
2011
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G. Bossard and H. Nicolai, Counterterms vs. Dualities , JHEP 08
2011
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R. Kallosh, N=8 Counterterms and E 7 ( 7 ) E_{7(7)} Current Conservation , JHEP 06
2011
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