D-branes, B-fields and twisted K-theory

TL;DR

This paper proposes a new classification of D-brane charges in string theory using twisted K-theory of C*-algebras, especially in the presence of non-trivial B-fields, aligning with Witten's approach for torsion cases.

Contribution

It introduces a novel framework for classifying D-brane charges via twisted K-theory of infinite dimensional C*-algebras, extending previous models.

Findings

D-brane charges are classified by twisted K-theory in the presence of B-fields.

The proposed classification coincides with Witten's for torsion B-fields.

Provides a mathematical foundation for D-brane charge classification in complex backgrounds.

Abstract

In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C^*-algebra. In the case of B-fields whose curvature is pure torsion our description is shown to coincide with that of Witten.