Cancellation of Conformal and Chiral Anomalies in $N \geq 5$   supergravities
  A cancellation of conformal anomalies in d=4 for the $C^2+\bar C^2$ and of chiral anomalies for the $C^2-\bar C^2$ is known in N-extended supergravities with $N \geq 5$. We propose an explanation of these cancellations using supersymmetry and dimension of linearized chiral superfields. We contrast these models with the ones with $N < 5$, where both types of anomalies are known to be present. 
Renata Kallosh
hep-th