Abstract
We generalize Cremmer-Julia 1st order action of mathcal{N}=8 supergravity with manifest E7(7) symmetry to cases of mathcal{N}=6 with manifest SO∗(12) and mathcal{N}=5 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 mathcal{N}ge 5 supergravitiesaredeformedbyacandidateUVdivergencetheghostfielddoesnot decouple. Therefore we argue that U duality and supersymmetry suggest an explanation of the mysterious cancellation of UV infinities at L = 4, mathcal{N}=5 in d=4. The same reasoning implies that, in absence of duality and supersymmetry anomalies, which still require a better understanding, mathcal{N}ge 5 perturbative supergravities may be UV finite at higher-loops.
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