Gerbes, (twisted) K-theory, and the supersymmetric WZW model

Abstract

The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifests itself in different equivalent ways. Besides the cohomological description as a DD class, it can be defined in terms of a family of local line bundles or as a prolongation problem for an (infinite-dimensional) principal bundle, with the fiber consisting of (a subgroup of) projective unitaries in a Hilbert space. The prolongation aspect is directly related to the appearance of central extensions of (broken) symmetry groups. We also discuss the construction of twisted K-theory classes by families of supercharges for the supersymmetric Wess-Zumino-Witten model.

arXiv commentsome typos corrected, a short comment in the end and two references added

References in corpus (4)

• Twisted K-theory and K-theory of bundle gerbes
• WZW branes and gerbes
• Index Theory, Gerbes, and Hamiltonian Quantization
• Twisted K-theory and loop groups

Cited by in corpus (9)

• K-Theory from a physical perspective
• E8 Gauge Theory and Gerbes in String Theory
• K-theoretical boundary rings in N=2 coset models
• The Loop Group of E8 and Targets for Spacetime
• Twisted K-theory of differentiable stacks
• Supersymmetric WZW models and twisted K-theory of SO(3)
• Families of Dirac operators and quantum affine groups
• NS Fivebrane and Tachyon Condensation
• On the relationship of gerbes to the odd families index theorem