The global gravitational anomaly of the self-dual field theory

TL;DR

This paper derives a formula for the global gravitational anomaly of the self-dual field theory on compact manifolds, revealing connections with determinant line bundles, theta functions, and applications to supergravity.

Contribution

It introduces a new formula for the gravitational anomaly of the self-dual field, linking mathematical structures with physical theories and applying it to supergravity.

Findings

Global gravitational anomaly formula derived

Anomaly vanishes in type IIB supergravity on 10D spin manifolds

Links between determinant line bundles, theta functions, and anomalies

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.