The global gravitational anomaly of the self-dual field theory

Details The global gravitational anomaly of the self-dual field theory The global gravitational anomaly of the self-dual field theory

2011-10-20

arxiv.org/abs/1110.4639v1

Physics

High Energy Physics

High Energy Physics - Theory

42 pages

Scientific paper

We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac operators, Siegel theta functions and a functor constructed by Hopkins and Singer. We apply our result to type IIB supergravity and show that in the naive approximation where the Ramond-Ramond fields are treated as differential cohomology classes, the global gravitational anomaly vanishes on all 10-dimensional spin manifolds. We sketch a few other important physical applications.

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