Anomalies in gauge theory and gerbes over quotient stacks

TL;DR

This paper offers a novel interpretation of the Faddeev-Mickelsson anomaly in Yang-Mills theories using S^1-central extensions of Lie groupoids, connecting gauge anomalies with geometric structures.

Contribution

It introduces a new geometric framework for understanding gauge anomalies via gerbes and groupoid extensions, advancing the mathematical description of anomalies.

Findings

Reformulation of the Faddeev-Mickelsson anomaly using gerbes and groupoids

Establishment of a link between gauge anomalies and S^1-central extensions

Potential implications for the geometric quantization of gauge theories

Abstract

We give a new interpretation of the Faddeev-Mickelsson anomaly in certain Yang-Mills theories in terms of S^1-central extensions of Lie groupoids.