E7(7) symmetry and finiteness of N=8 supergravity

We study N = 8 supergravity deformed by the presence of the candidate counterterms. We show that even though they are invariant under undeformed E-7(7), all of the candidate counterterms violate the deformed E-7(7) current conservation. The same conclusion follows from the uniqueness of the Lorentz and SU(8) covariant, E-7(7) invariant unitarity constraint expressing the 56-dimensional E-7(7) doublet via 28 independent vectors, in agreement with the E-7(7)/SU(8) coset space geometry. Therefore E-7(7) duality predicts the all-loop UV finiteness of perturbative N = 8 supergravity.