Closed form effective conformal anomaly actions in D ≥ 4

I present, in any D greater than or equal to 4, closed-form type B conformal anomaly effective actions incorporating the logarithmic scaling cutoff dependence that generates these anomalies. Their construction is based on a novel class of Weyl-invariant tensor operators. The only known type A actions in D greater than or equal to 4 are extensions of the Polyakov integral in D = 2, despite contrary appearances, we show that their nonlocality does not conflict with general anomaly requirements. They are, however, physically unsatisfactory, prompting a brief attempt at better versions. (C) 2000 Elsevier Science B.V. All rights reserved.