Higher Gauge Theory: 2-Connections on 2-Bundles
| dc.creator | Baez, John | |
| dc.creator | Schreiber, Urs | |
| dc.date | 2004-12-30 | |
| dc.date.accessioned | 2026-07-07T04:17:54Z | |
| dc.date.available | 2026-07-07T04:17:54Z | |
| dc.description | Connections and curvings on gerbes are beginning to play a vital role in differential geometry and mathematical physics -- first abelian gerbes, and more recently nonabelian gerbes. These concepts can be elegantly understood using the concept of `2-bundle' recently introduced by Bartels. A 2-bundle is a generalization of a bundle in which the fibers are categories rather than sets. Here we introduce the concept of a `2-connection' on a principal 2-bundle. We describe principal 2-bundles with connection in terms of local data, and show that under certain conditions this reduces to the cocycle data for nonabelian gerbes with connection and curving subject to a certain constraint -- namely, the vanishing of the `fake curvature', as defined by Breen and Messing. This constraint also turns out to guarantee the existence of `2-holonomies': that is, parallel transport over both curves and surfaces, fitting together to define a 2-functor from the `path 2-groupoid' of the base space to the structure 2-group. We give a general theory of 2-holonomies and show how they are related to ordinary parallel transport on the path space of the base manifold. | |
| dc.description | 73 pp, 4 eps figures | |
| dc.identifier | https://arxiv.org/abs/hep-th/0412325 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0412325 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52955 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Higher Gauge Theory: 2-Connections on 2-Bundles | |
| dc.type | text |