Closed form effective conformal anomaly actions in D ≥ 4

Abstract

I present, in any D≥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≥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.