Higher Gauge Theory
| dc.creator | Baez, John C. | |
| dc.creator | Schreiber, Urs | |
| dc.date | 2005-11-29 | |
| dc.date | 2006-06-28 | |
| dc.date.accessioned | 2026-07-07T09:41:42Z | |
| dc.date.available | 2026-07-07T09:41:42Z | |
| dc.description | Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings) using 2-connections on 2-bundles. A 2-bundle is a categorified version of a bundle: that is, one where the fiber is not a manifold but a category with a suitable smooth structure. Where gauge theory uses Lie groups and Lie algebras, higher gauge theory uses their categorified analogues: Lie 2-groups and Lie 2-algebras. We describe a theory of 2-connections on principal 2-bundles and explain how this is related to Breen and Messing's theory of connections on nonabelian gerbes. The distinctive feature of our theory is that a 2-connection allows parallel transport along paths and surfaces in a parametrization-independent way. In terms of Breen and Messing's framework, this requires that the "fake curvature" must vanish. In this paper we summarize the main results of our theory without proofs. | |
| dc.description | 10 encapsulated Postscript figures | |
| dc.identifier | https://arxiv.org/abs/math/0511710 | |
| dc.identifier | http://arxiv.org/abs/math/0511710 | |
| dc.identifier | In Categories in Algebra, Geometry and Mathematical Physics, eds. A. Davydov et al, Contemp. Math. 431, AMS, Providence, Rhode Island, 2007, pp. 7-30 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161920 | |
| dc.subject | Differential Geometry | |
| dc.subject | Category Theory | |
| dc.title | Higher Gauge Theory | |
| dc.type | text |