The index of a local boundary value problem for strongly Callias-type operators

TL;DR

This paper extends an index theorem to non-compact manifolds with boundary for strongly Callias-type operators, offering new insights into the Horava-Witten anomaly.

Contribution

It generalizes Freed's index theorem to non-compact manifolds with boundary for strongly Callias-type operators.

Findings

Computed the index for local boundary value problems on non-compact manifolds.

Extended Freed's index theorem to a broader class of manifolds.

Provided new mathematical insights into the Horava-Witten anomaly.

Abstract

We consider a complete Riemannian manifold M whose boundary is a disjoint union of finitely many complete connected Riemannian manifolds. We compute the index of a local boundary value problem for a strongly Callias-type operator on M. Our result extends an index theorem of D. Freed to non-compact manifolds, thus providing a new insight on the Horava-Witten anomaly.