Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 8

Higher gauge theory with string 2-groups

Pages: 1895 – 1952

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

Authors

Getachew Alemu Demessie (Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland, United Kingdom)

Christian Sämann (Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland, United Kingdom)

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.

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Published 29 March 2018