Contents Online

# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 8

### Higher gauge theory with string 2-groups

Pages: 1895 – 1952

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n8.a2

#### Authors

#### 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 $\textsf{Bibun}$ of Lie groupoids, bibundles and bibundle morphisms. We then construct categories internal to $\textsf{Bibun}$, which allow us to define principal 2-bundles with 2-groups internal to $\textsf{Bibun}$ 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.

Published 29 March 2018