Higher gauge theory with string 2-groups. (English) Zbl 1460.81058
Summary: 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 \(\mathsf{Bibun}\) of Lie groupoids, bibundles and bibundle morphisms. We then construct categories internal to \(\mathsf{Bibun}\), which allow us to define principal 2-bundles with 2-groups internal to \(\mathsf{Bibun}\) 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.
MSC:
81T13 | Yang-Mills and other gauge theories in quantum field theory |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
17B81 | Applications of Lie (super)algebras to physics, etc. |
22A22 | Topological groupoids (including differentiable and Lie groupoids) |