Closed Form Effective Conformal Anomaly Actions in D$\geq$4

TL;DR

This paper derives closed-form effective actions for type B conformal anomalies in dimensions four and higher, using Weyl-invariant tensors, and discusses their properties and limitations.

Contribution

It introduces a novel class of Weyl-invariant tensor operators to construct explicit anomaly actions in D≥4, extending previous approaches.

Findings

Derived explicit form of type B anomaly actions in D≥4

Showed nonlocality of known type A actions does not conflict with anomalies

Discussed limitations and potential improvements of these actions

Abstract

I present, in any D$\geq$4, closed-form type B conformal anomaly effective actions incorporating the logarithmic scaling cutoff dependence that generates these anomalies. Their construction is based on a novel class of Weyl-invariant tensor operators. The only known type A actions in D$\geq$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.