The global gravitational anomaly of the self-dual field theory

Abstract

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.

42 pages. v2: Typos corrected. Version accepted for publication in CMP

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• Heisenberg Groups and Noncommutative Fluxes
• Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
• Fivebrane instantons and Calabi-Yau fourfolds with flux
• The Picard group of the moduli space of curves with level structures
• The partition bundle of type A_{N-1} (2, 0) theory
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Cited by in corpus (6)

• IIB flux non-commutativity and the global structure of field theories
• The anomaly that was not meant IIB
• Remarks on the Green-Schwarz terms of six-dimensional supergravity theories
• A Modern Point of View on Anomalies
• The global anomalies of (2,0) superconformal field theories in six dimensions
• Hamiltonian anomalies from extended field theories