The Faddeev-Mickelsson-Shatashvili anomaly and lifting bundle gerbes

TL;DR

This paper investigates the Faddeev-Mickelsson-Shatashvili anomaly in gauge theory, using bundle gerbes to describe the obstruction to lifting gauge group actions, and provides multiple equivalent formulations.

Contribution

It introduces a novel perspective on the anomaly through the framework of bundle gerbes and relates it to the caloron correspondence.

Findings

Equivalent descriptions of the anomaly as lifting bundle gerbes.

Connection between the anomaly and caloron correspondence.

Clarification of the geometric nature of the obstruction.

Abstract

In gauge theory, the Faddeev-Mickelsson-Shatashvili anomaly arises as a prolongation problem for the action of the gauge group on a bundle of projective Fock spaces. In this paper, we study this anomaly from the point of view of bundle gerbes and give several equivalent descriptions of the obstruction. These include lifting bundle gerbes with non-trivial structure group bundle and bundle gerbes related to the caloron correspondence.