Surface holonomy and gauge 2-group

TL;DR

This paper explores the mathematical framework of surface holonomies for string-like objects, using 2-groups derived from different connection pairs, advancing the understanding of higher gauge theories.

Contribution

It compares two methods of constructing surface holonomies, both resulting in 2-group structures, enriching the mathematical tools for higher gauge theories.

Findings

Both methods produce consistent 2-group structures.

The approach using pairs of one and two form connections offers a new perspective.

The second method with two one-form connections simplifies the construction.

Abstract

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category theoretic generalization of the gauge group, called a 2-group. I consider two different ways of constructing surface holonomies, one by using a pair of one and two form connections, and another by using a pair of one-form connections. Both procedures result in the structure of a 2-group.