Gerbes and quantum field theory

TL;DR

This paper explains how gerbes naturally appear in quantum field theory, especially with chiral fermions, and explores their relation to gauge group extensions and index theory for classifying these structures.

Contribution

It provides a detailed explanation of the emergence of gerbes in quantum field theory and their connection to gauge group extensions and index theory.

Findings

Gerbes arise in quantum field theory, particularly with chiral fermions.

The role of gauge group extensions in gerbe formation is clarified.

Index theory is used to compute the Dixmier-Douady class of a gerbe.

Abstract

The basic mechanism how gerbes arise in quantum field theory is explained; in particular the case of chiral fermions in background fields is treated. The role of of various gauge group extensions (central extensions of loop groups and their generalizations) is also explained, in relation to index theory computation of the Dixmier-Douady class of a gerbe.