Higher bundle gerbes and cohomology classes in gauge theories

TL;DR

This paper introduces higher bundle gerbes as a geometric tool to realize higher degree integral cohomology, with examples from infinite-dimensional gauge theory spaces.

Contribution

It presents the concept of higher bundle gerbes and applies it to infinite-dimensional gauge theory contexts, providing new geometric insights.

Findings

Higher bundle gerbes realize higher cohomology classes.

Application to gauge theory spaces demonstrates practical relevance.

Provides a geometric framework for higher cohomology in physics.

Abstract

The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.