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A vanishing theorem for the conformal anomaly in dimension $ >2$


Authors: Jack Morava and Hirotaka Tamanoi
Journal: Proc. Amer. Math. Soc. 100 (1987), 767-774
MSC: Primary 58G10; Secondary 53C80, 58D17, 81E20
DOI: https://doi.org/10.1090/S0002-9939-1987-0894452-4
MathSciNet review: 894452
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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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DOI: https://doi.org/10.1090/S0002-9939-1987-0894452-4
Article copyright: © Copyright 1987 American Mathematical Society

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