We generalize Cremmer-Julia 1st order action of N=8\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}=8 $$\end{document} supergravity with manifest E7(7) symmetry to cases of N=6\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}=6 $$\end{document} with manifest SO∗(12) and N=5\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}=5 $$\end{document} with manifest SU(1, 5) duality symmetries. These U dualities belong to groups of type E7 which do not admit a symmetric bilinear invariant for vector fields. Therefore the 2d order classical action derived from the one with manifest E7 type duality has a ghost vector field which, under appropriate boundary conditions, decouples. We show that when classical N≥5\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}\ge 5 $$\end{document} supergravitiesaredeformedbyacandidateUVdivergencetheghostfielddoesnot decouple. Therefore we argue that U duality and supersymmetry suggest an explanation of the mysterious cancellation of UV infinities at L = 4, N=5\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}=5 $$\end{document} in d=4. The same reasoning implies that, in absence of duality and supersymmetry anomalies, which still require a better understanding, N≥5\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{N}\ge 5 $$\end{document} perturbative supergravities may be UV finite at higher-loops.
