Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 019, 41 pages      arXiv:0912.3757

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

Spyros Alexakis
Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Canada

Received April 01, 2010, in final form February 15, 2011; Published online February 26, 2011

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.

Key words: conformal geometry; renormalized volume; global invariants; Deser-Schwimmer conjecture.

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