On a possibility of a UV finite N=8 supergravity

We compare the local Lorentz covariant all-loop counterterms built in the 4+32 on shell superspace of N=8 supergravity with those evaluated in the 4+16 light-cone superspace. We find that the on-shell light-cone counterterms for the amplitudes in all order loops break Lorentz covariance, unless the coefficient in front of them vanishes. This leads to a prediction that all-loop UV infinities should be absent in the gauge-independent computation of the perturbative S-matrix. Here we rely on the validity of the equivalence theorem for the S-matrix in the light-cone gauge and Lorentz covariant gauges, which requires the absence of anomalies in quantum perturbation theory.