The decomposition of Global Conformal Invariants V

TL;DR

This paper advances the proof of a conjecture on the structure of global conformal invariants, showing they can be decomposed into simpler geometric components, with algebraic simplifications aiding the overall proof.

Contribution

It simplifies the algebraic framework needed to prove the conjecture, focusing on reducing complex algebraic results to basic lemmas for future completion.

Findings

Reduction of algebraic complexity in conformal invariants

Simplification of key lemmas for the conjecture's proof

Progress towards a complete proof of the Deser-Schwimmer conjecture

Abstract

This is the fifth in a series of papers 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. The present paper complements [6] in reducing the purely algebraic results that were used in [3,4 to certain simpler Lemmas, which will be proven in the last paper in this series, [8].