Abstract
We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian \( \mathcal{N}=\left(2,0\right) \) tensor multiplet taking values in a semistrict Lie 2-algebra.
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Jurčo, B., Sämann, C. & Wolf, M. Semistrict higher gauge theory. J. High Energ. Phys. 2015, 87 (2015). https://doi.org/10.1007/JHEP04(2015)087
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DOI: https://doi.org/10.1007/JHEP04(2015)087