Adjusted connections on non-abelian bundle gerbes

TL;DR

This paper develops a comprehensive theory of adjusted connections on non-abelian bundle gerbes, addressing challenges in higher gauge theory and providing a coordinate-independent formulation of a lifting theorem.

Contribution

It introduces a new framework for adjusted connections on non-abelian bundle gerbes, classified by an adjusted non-abelian differential cohomology, and relates them to abelian bundle 2-gerbes.

Findings

Established a classification of adjusted connections via adjusted non-abelian differential cohomology.

Provided a coordinate-independent formulation of Tellez-Dominguez' lifting theorem.

Linked adjusted non-abelian connections to connections on abelian bundle 2-gerbes.

Abstract

Higher gauge theory for non-abelian structure 2-groups faces significant challenges when extending beyond the fake-flat sector, which suffers from limited applicability in physical models. A promising resolution involves equipping 2-groups with additional structure, known as adjustments. We present a comprehensive theory of adjusted connections on non-abelian bundle gerbes, classified by Saemann's adjusted version of non-abelian differential cohomology. This theory enables, in particular, a new coordinate-independent formulation of Tellez-Dominguez' lifting theorem, establishing a correspondence between adjusted connections on non-abelian bundle gerbes and connections on abelian bundle 2-gerbes.