The Decomposition of Global Conformal Invariants: Some Technical Proofs. I

TL;DR

This paper provides technical proofs for a conjecture on the algebraic structure of global conformal invariants, showing they can be decomposed into simpler geometric components.

Contribution

It offers rigorous proofs confirming the Deser-Schwimmer conjecture on the structure of conformally invariant integrals of geometric scalars.

Findings

Confirmed the decomposition of global conformal invariants into local invariants, divergences, and Chern-Gauss-Bonnet terms.

Established the algebraic structure of conformal invariants through detailed proofs.

Advanced understanding of geometric invariants in conformal geometry.

Abstract

This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of "global conformal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand.