# Conformal Anomaly and Off-Shell Extensions of Gravity

## TL;DR

This paper investigates the gauge dependence of conformal anomalies in supergravity theories, proposing a criterion for the correct gauge choice that ensures anomaly consistency and showing that anomaly cancellation is only possible in extended supergravities with N≥5.

## Contribution

It introduces a gauge selection criterion based on Wess-Zumino consistency to resolve anomalies and demonstrates that anomaly cancellation occurs only in supergravities with N≥5.

## Key findings

- Correct gauge choice removes anomaly-violating terms.
- Anomaly cancellation is only possible for N≥5 supergravities.
- The link between anomalies and divergences depends on gauge choice.

## Abstract

The gauge dependence of the conformal anomaly for spin 3/2 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 $N\geq 5$.