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Baez and Schreiber: Higher Gauge Theory

  1. Nov 29, 2005 #1

    marcus

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    http://arxiv.org/abs/math.DG/0511710
    Higher Gauge Theory
    John C. Baez, Urs Schreiber
    10 figures
    Differential Geometry; Category Theory

    "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."
     
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  3. Nov 29, 2005 #2

    Kea

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    Ah! Very nice. :approve:
     
  4. Nov 29, 2005 #3

    marcus

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    glad you are pleased, Kea
    (thought you would be delighted:smile: )

    BTW
    I see that Hamburg has made an honest mathematician out of Urs!
    he is listed as in the Math Department there.
     
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