A classification of global conformal invariants**Dedicated to the memory of our colleague Christian Duval 1947–2018.

Abstract

We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e. scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local Weyl rescalings of the metric. We use cohomological techniques that have already proved instrumental in the classification of Weyl anomalies in arbitrary dimensions. The approach we follow is purely algebraic and borrows techniques originating from perturbative quantum field theory for which locality is crucial.