Explicit String bundles

TL;DR

This paper presents a method to construct explicit examples of higher string bundles, specifically 2-bundles with the String 2-group structure, over homogeneous spaces, including detailed formulas for a specific case.

Contribution

It introduces a new construction method for non-abelian 2-bundles with String 2-group structure and provides explicit formulas for their cocycles.

Findings

Constructed many examples over homogeneous spaces

Provided explicit formulas for a specific 2-bundle example

Enhanced understanding of higher gauge theory structures

Abstract

While higher bundles are of clear relevance to higher gauge theory, examples other than abelian bundle gerbes are hard to come across. One would in particular like to see 2-bundles where the structure 2-group is the String 2-group associated to a compact simple simply-connected Lie group. This talk will outline a method to construct many examples over homogeneous spaces. We shall also consider one example in detail, giving explicit formulas for the crossed-module-valued Cech cocycle arising from a local trivialisation.