The decomposition of Global Conformal Invariants I: On a conjecture of Deser and Schwimmer

2007/11/11 by Spyros Alexakis, Alexakis, Spyros · 1 citation
Mathematics · Physics and Astronomy · #53C #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0711.1685

openalex publication_date 2007/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal 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. In this paper we set up an iterative procedure that proves the decom- position. We then derive the iterative step in the first of two cases, subject to a purely algebraic result which is proven in [6, 7, 8].

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