Bundle gerbes and surface holonomy

  • Jürgen Fuchs

    Karlstads Universitet, Sweden
  • Thomas Nikolaus

    Universität Regensburg, Germany
  • Christoph Schweigert

    Universität Hamburg, Germany
  • Konrad Waldorf

    University of California, Berkeley, USA
Bundle gerbes and surface holonomy cover
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Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes under descent. Inspired by structures arising in a representation theoretic approach to rational conformal field theories, we introduce geometric structure that is appropriate to define surface holonomy in more general situations: Jandl gerbes for unoriented surfaces, D-branes for surfaces with boundaries, and bi-branes for surfaces with defect lines.