Constraining gravitational interactions in the M theory effective action

I shall discuss constraints on the terms of the form D^{2k} R^4 in the effective action of M theory for certain low values of k. These interactions, which are non-BPS for k greater than 3, are argued to be non-vanishing only for certain values of k, based on certain assumptions of the structure of supersymmetry. The constraints on these interactions are obtained from the perturbative structure of string amplitudes, based on duality and supersymmetry.