The generalization of scale invariance when gravitational effects are
    considered is Weyl invariance, namely, invariance under (global or local)
    rescalings of the metric. In this work, we discuss in some details the
    implications of the fact that the value of the anomaly for the global Weyl
    invariant coupling of scalar fields to gravity is sensitive to the dynamics (or
    absence thereof) of the gravitational field.

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