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 Cech 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 Severa. 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 N=(2,0) tensor multiplet taking values in a semistrict Lie 2-algebra.
Highlights
We develop semistrict higher gauge theory from first principles
We further derive the full description of connective structures on semistrict principal 2bundles including the non-linear gauge transformations
The higher Maurer-Cartan forms are incorporated abstractly as constrained parameters into the gauge transformation. This is not the case in our approach; our detailed understanding of the differential cohomology underlying semistrict principal 2-bundles with connective structures makes the parameters of gauge transformations explicit
Summary
Gauge theory is one of the most far-reaching concepts in modern theoretical physics as is exemplified by the impressive success of the standard model of elementary particles as well as many of the more recent developments in string theory such as the gauge/gravity correspondence. We shall see that semistrict principal 2bundles will allow for incorporating cubic terms in the connection 1-form in the definition of the 3-form curvature Another popular approach to deriving a classical description of the (2, 0)-theory is based on a non-Abelian generalisation of the tensor hierarchy [13,14,15,16,17] with the closely related proposals of [18, 19]. The higher Maurer-Cartan forms are incorporated abstractly as constrained parameters into the gauge transformation This is not the case in our approach; our detailed understanding of the differential cohomology underlying semistrict principal 2-bundles with connective structures makes the parameters of gauge transformations explicit
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