Higher Gauge Theory with String 2-Groups

TL;DR

This paper provides a comprehensive framework for higher gauge theory using the string 2-group, including explicit constructions, differentiation to Lie 2-algebras, and applications to non-abelian self-dual strings.

Contribution

It introduces a complete description of higher gauge theory with the string 2-group, including explicit models, differentiation to Lie 2-algebras, and the formulation of non-abelian self-dual strings.

Findings

Explicit construction of principal 2-bundles with string 2-group

Lie differentiation yields the string Lie 2-algebra

Development of higher non-abelian Deligne cohomology

Abstract

We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak 2-category Bibun of Lie groupoids, bibundles and bibundle morphisms. We then construct categories internal to Bibun, which allow us to define principal 2-bundles with 2-groups internal to Bibun as structure 2-groups. Using these, we Lie-differentiate the 2-group model of the string group and we obtain the well-known string Lie 2-algebra. Generalizing the differentiation process, we find Maurer-Cartan forms leading us to higher non-abelian Deligne cohomology, encoding the kinematical data of higher gauge theory together with their (finite) gauge symmetries. We end by discussing an example of non-abelian self-dual strings in this setting.