Gerbes in Geometry, Field Theory, and Quantisation

• Main Author: Bunk Severin
• Format: Article
• Language: English
• Published: De Gruyter 2021-06-01
• Series: Complex Manifolds
• Subjects: bundle gerbes; higher geometry; functorial field theory; wzw model; 2-plectic geometry; derived geometric quantisation; 53c08; 53d50; 57r56
• Online Access: https://doi.org/10.1515/coma-2020-0112

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.