From gauge anomalies to gerbes and gerbal actions

TL;DR

This paper explores the connections between gerbes, gerbal actions, and quantum field theory anomalies, highlighting how classical obstruction theory unifies these advanced mathematical and physical concepts.

Contribution

It establishes a link between gerbes, gerbal actions, and quantum anomalies through classical obstruction theory, providing a new perspective on gauge group extensions.

Findings

Gerbes and gerbal actions relate to quantum anomalies and gauge extensions.

Classical obstruction theory unifies higher categorical and quantum field theory concepts.

New insights into the mathematical structure of gauge anomalies.

Abstract

The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies, gauge group extensions, and 3-cocycles. The unifying concept is the classical obstruction theory for group extensions as explained in the reference [ML].