It has been argued by Witten and others that in the presence of a nontrivial
B-field, D-brane charges in type IIB string theories are measured by twisted
K-theory. In joint work with Bouwknegt, Carey and Murray it was proved that
twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose
elements are ordinary vector bundles on a principal projective unitary bundle,
with an action of the bundle gerbe determined by the principal projective
unitary bundle. The principal projective unitary bundle is in turn determined
by the twist. In this paper, we study in more detail the Chern-Weil
representative of the Chern character of bundle gerbe K-theory that was
introduced previously, and we also extend it to the equivariant and holomorphic
cases. Included is a discussion of interesting examples.Comment: 24 pages, Latex2e. To appear in CM
