Geometric and topological aspects of Type IIB D-branes

TL;DR

This paper explores the geometric and topological properties of Type IIB D-branes, focusing on their classification via (twisted) K-theory and the implications of anomalies and background fields in string theory.

Contribution

It provides an introduction to the use of twisted K-theory and noncommutative geometry in classifying D-brane charges, extending classical formulas to more complex scenarios.

Findings

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

Noncommutative geometry offers a framework for generalizing charge formulas.

The paper introduces the mathematical background necessary for these classifications.

Abstract

In string theory D-branes can be classified by the RR-charge they carry. In the simplest case the quantized RR-charge takes values in K-theory of the spacetime manifold. However, if the D-brane worldvolume is not spin^c or if there is a background B-field present, the Freed-Witten anomaly cancellation condition requires the RR-charge to take values in twisted K-theory. Twisted K-theory can be defined using the language of noncommutative geometry, thus opening up a possibility for noncommutative generalizations, in particular of the Minasian-Moore formula for the classical approximation of the charge (as was done in arXiv:hep-th/0607020v3). A friendly introduction to these topics is given.