A vanishing theorem for the conformal anomaly in dimension >2

Morava, Jack; Tamanoi, Hirotaka

doi:10.1090/S0002-9939-1987-0894452-4

A vanishing theorem for the conformal anomaly in dimension $>2$
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by Jack Morava and Hirotaka Tamanoi PDF

Proc. Amer. Math. Soc. 100 (1987), 767-774 Request permission

Abstract:

We examine the conformal anomaly of quantum field theory in the light of Atiyah and Singer’s recent work on the chiral anomaly. We show that the bundle over the space of conformal structures defined on a given manifold, constructed as the index of the conformally invariant family of Laplace operators, is a torsion class in real $K$-theory, Indeed, its Chern forms are zero. These Chern forms transgress to define classes in certain local cohomology groups calculated recently by Bonora, Cotta-Ramusino, and Reina; a corollary is that, although these obstruction groups are nonzero, the obstruction to the existence of a gauge-covariant propagator for the Laplace operator is the trivial element of obstruction group.

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