A classification of global conformal invariants

TL;DR

This paper classifies all scalar densities that remain invariant under local Weyl rescalings across various dimensions, using algebraic cohomological methods from quantum field theory.

Contribution

It provides a comprehensive algebraic classification of global conformal invariants in arbitrary dimensions, extending previous work on Weyl anomalies.

Findings

Complete classification in even and odd dimensions

Use of cohomological techniques from quantum field theory

Algebraic approach emphasizing locality

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.