  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.
