Higher Gauge Theory

dc.creatorBaez, John C.
dc.creatorSchreiber, Urs
dc.date2005-11-29
dc.date2006-06-28
dc.date.accessioned2026-07-07T09:41:42Z
dc.date.available2026-07-07T09:41:42Z
dc.descriptionJust 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.description10 encapsulated Postscript figures
dc.identifierhttps://arxiv.org/abs/math/0511710
dc.identifierhttp://arxiv.org/abs/math/0511710
dc.identifierIn 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.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161920
dc.subjectDifferential Geometry
dc.subjectCategory Theory
dc.titleHigher Gauge Theory
dc.typetext

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