Tree amplitudes and two-loop counterterms in D=11 supergravity - art. no. 084010

We compute the tree level 4-particle bosonic scattering amplitudes in D = 1 1 supergravity. By construction, they are part of a linearized supersymmetr y, coordinate, and 3-form gauge invariant. While this on-shell invariant is nonlocal, suitable SUSY-preserving differentiations turn it into a local o ne with correct dimension to provide a natural lowest (two-loop) order coun terterm candidate. Its existence shows explicitly that no symmetries protec t this ultimate supergravity: Indeed this invariant, together with the rece ntly calculated infinite coefficient of its 4-graviton part, constitutes a demonstration of two-loop non-renormalizability.