N=8 supergravity on the light cone

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on the unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 quantum field theory path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are nonlocal in transverse directions for the diagrams with the number of loops smaller than at least n+3. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. Using the E7(7) symmetry we argue that the light-cone supergraphs predict all-loop finiteness of d=4 N=8 supergravity.