The Global Gravitational Anomaly of the Self-dual Field Theory |
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| Authors: | Samuel Monnier |
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| Institution: | 1. Laboratoire de Physique Théorique de l’école Normale Supérieure (Unité mixte de recherche du CNRS et de l’ENS, associée à l’Université Pierre et Marie Curie et aux fédérations de recherche FR684 et FR2687), CNRS UMR 8549, 24 rue Lhomond, 75231, Paris Cedex 05, France
2. Laboratoire de Physique Théorique et Hautes énergies, CNRS UMR 7589 and Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, 75252, Paris Cedex 05, France
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| 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. |
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