Chern character in twisted K-theory: equivariant and holomorphic cases

TL;DR

This paper explores the Chern character in twisted K-theory, extending its representation to equivariant and holomorphic cases, with implications for understanding D-brane charges in string theory.

Contribution

It provides a detailed study of the Chern-Weil representative of the Chern character in bundle gerbe K-theory, extending it to equivariant and holomorphic contexts.

Findings

Extended Chern character to equivariant and holomorphic cases

Connected twisted K-theory with bundle gerbe K-theory

Discussed examples illustrating the theory

Abstract

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.