Explicit Non-Abelian Gerbes with Connections

Understand

We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group.

• Most importantly, we depart from the common fake-flat connections and employ adjusted connections.
• This is an important generalisation that is needed for physical applications especially in the context of supergravity.
• We give a number of explicit examples; in particular, we lift the spin structure on $S^4$, corresponding to an instanton-anti-instanton pair, to a string structure, a 2-group bundle with connection.