**
Samuel Monnier
**

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

**Abstract
**

We will report on recent work on the global gravitational anomaly of the self-dual field theory (also called the abelian chiral p-form). The partition function of the self-dual field theory on a 4k+2 dimensional manifold M is a section of a certain line bundle over the space of metrics on M modulo diffeomorphisms. We will describe the isomorphism class of this bundle and propose a conjectural formula for the holonomy of a natural connection living on it. Mathematically, this story provides an interesting link between the theory of determinant line bundles of Dirac operators, Siegel theta functions and certain cobordism invariants defined by Hopkins and Singer.