Conformal anomaly and off-shell extensions of gravity

The gauge dependence of the conformal anomaly for spin-3/2 and spin-2 fields in nonconformal supergravities has been a long standing puzzle. In this paper we argue that the ``correct'' gauge choice is the one that follows from requiring all terms that would imply a violation of the Wess-Zumino consistency condition to be absent in the counterterm, because otherwise the usual link between the anomaly and the one-loop divergence becomes invalid. Remarkably, the ``good'' choice of gauge is the one that confirms our previous result [K. A. Meissner and H. Nicolai, Phys. Lett. B 772, 169 (2017).] that a complete cancellation of conformal anomalies in $D=4$ can only be achieved for N-extended (Poincar\'e) supergravities with N≥5.