A cancellation of conformal anomalies in $d=4$ for the $C^2+{\overline{C}}^2$ and of chiral anomalies for the $C^2-{\overline{C}}^2$ is known in $\mathcal{N}$-extended supergravities with $\mathcal{N}\ge 5$. We propose an explanation of these cancellations using supersymmetry and dimension of linearized chiral superfields. We contrast these models with the ones with $\mathcal{N}<5$, where both types of anomalies are known to be present.

• Received 4 January 2017

DOI:https://doi.org/10.1103/PhysRevD.95.041701