E{7(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. Therefore E{7(7)} duality predicts the all-loop UV finiteness of perturbative N=8 supergravity. 
Renata Kallosh
hep-th gr-qc