# Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

@article{Aschieri2005NonabelianBG, title={Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory}, author={Paolo Aschieri and Luigi Cantini and Branislav Jur{\vc}o}, journal={Communications in Mathematical Physics}, year={2005}, volume={254}, pages={367-400} }

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with 2-form gauge potential.

## 101 Citations

Crossed module bundle gerbes; classification, string group and differential geometry

- Mathematics, Physics
- 2011

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to a (Lie) crossed module (H → D) there is a simplicial group , the nerve of the groupoid…

Differential Geometry of Gerbes and Differential Forms

- Mathematics, Physics
- 2011

We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes due to W. Messing and the author [5], and give a more direct derivation of the associated…

Nonabelian bundle 2-gerbes

- Mathematics, Physics
- 2009

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called…

Non-abelian gerbes and some applications in string theory

- Physics, Mathematics
- 2018

We review a systematic construction of the 2-stack of bundle gerbes via descent, and extend it to non-abelian gerbes. We review the role of non-abelian gerbes in orientifold sigma models, for the…

Parallel transport in principal 2-bundles

- Mathematics, Physics
- 2017

A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local…

Principal 2-bundles and their gauge 2-groups

- Mathematics
- 2008

Abstract In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Čech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued…

Surface holonomy for non-abelian 2-bundles via double groupoids

- Mathematics
- 2011

In the context of non-abelian gerbes, we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We address their two-dimensional parallel transport, study its…

FOUR EQUIVALENT VERSIONS OF NONABELIAN GERBES

- Mathematics, Physics
- 2011

We recall and partially expand four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are…

Non-abelian differentiable gerbes

- Mathematics, Physics
- 2009

Abstract We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid G-extensions, which we call…

A Cubical Set Approach to 2-Bundles with Connection and Wilson Surfaces

- Mathematics, Physics
- 2010

In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We define their two-dimensional parallel transport, study its…

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