Bundle Gerbes and Surface Holonomy

Abstract

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.

25 pages

References in corpus (12)

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• WZW branes and gerbes
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• Bi-branes: Target Space Geometry for World Sheet topological Defects
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• Categorification and correlation functions in conformal field theory
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Cited by in corpus (10)

• A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories
• The CATS Service: an Astrophysical Research Tool
• Connections on non-abelian Gerbes and their Holonomy
• Magnetic Dirac-harmonic maps
• The three-dimensional origin of the classifying algebra
• Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
• Symmetries and defects in three-dimensional topological field theory
• Twisted K-theory and obstructions against positive scalar curvature metrics
• Survey of mathematical foundations of QFT and perturbative string theory
• Gerbes in Geometry, Field Theory, and Quantisation