  Supersymmetric higher derivative gravities define superconformal field
theories via the AdS/CFT correspondence. From the boundary theory viewpoint,
supersymmetry implies a relation between the coefficients which determine the
three point function of the stress energy tensor which can be tested in the
dual gravitational theory. We use this relation to formulate a necessary
condition for the supersymmetrization of higher derivative gravitational terms.
We then show that terms quadratic in the Riemann tensor do not present
obstruction to supersymmetrization, while generic higher order terms do. For
technical reasons, we restrict the discussion to seven dimensions where the
obstruction to supersymmetrization can be formulated in terms of the
coefficients of Weyl anomaly, which can be computed holographically.
