Cancellation of conformal and chiral anomalies in N≥5 supergravities

Abstract

A cancellation of conformal anomalies in $d=4$ for the ${C}^{2}+{\overline{C}}^{2}$ and of chiral anomalies for the ${C}^{2}\ensuremath{-}{\overline{C}}^{2}$ is known in $\mathcal{N}$-extended supergravities with $\mathcal{N}\ensuremath{\ge}5$. 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.