Gerbes in Geometry, Field Theory, and Quantisation

Abstract

This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted symplectic forms. This generalises earlier applications of gerbes to the prequantisation of quasi-symplectic groupoids.

38 pages; v2: References added and updated

References in corpus (12)

• Higher Topos Theory
• Bi-branes: Target Space Geometry for World Sheet topological Defects
• More Morphisms between Bundle Gerbes
• Higher Symplectic Geometry
• Constructions with bundle gerbes
• Bundle Gerbes and Surface Holonomy
• Twisted bundles and twisted K-theory
• Global gauge anomalies in two-dimensional bosonic sigma models
• Infinitesimal Symmetries of Dixmier-Douady Gerbes
• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Bundle gerbes on supermanifolds