Conformal Anomaly and Off-Shell Extensions of Gravity

The gauge dependence of the conformal anomaly for spin-3 and spin-2 fields in non-conformal supergravities has been a long standing puzzle. In this Letter 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 that a complete cancellation of conformal anomalies in D = 4 can only be achieved for N-extended (Poincar ́e) supergravities with N >=5.