Global Worldsheet Anomalies from M-Theory

TL;DR

This paper provides an M-theory proof of the Freed-Witten anomaly, linking it to K-theory and elucidating the origin of D6-brane gauge field quantization shifts.

Contribution

It offers a novel M-theory derivation of the Freed-Witten anomaly and connects it to K-theory classification of Ramond-Ramond fields.

Findings

Derived a localization formula using a U(1)-index theorem.

Linked the anomaly to K-theory classification.

Explored the M-theory origin of D6-brane effective action.

Abstract

We present an M-theory proof of the anomaly of Freed and Witten which in general shifts the quantisation law for the U(1) gauge field on a D6-brane. The derivation requires an understanding of how fields on the D6-brane lift to M-theory, together with a localisation formula which we prove using a U(1)-index theorem. We also show how the anomaly is related to the K-theory classification of Ramond-Ramond fields. In addition we discuss the M-theory origin of the D6-brane effective action, and illustrate the general arguments with a concrete example.