Topics on D-brane charges with B-fields

TL;DR

This paper reviews how K-theory classifies D-brane charges in string theory, especially with B-fields, highlighting the physical implications and analyzing the D6-brane as a non-abelian monopole.

Contribution

It provides an expository account of the role of K-theory and twisted K-groups in classifying D-brane charges with B-fields, connecting mathematical structures to physical phenomena.

Findings

K-theory classifies RR-charges in type II string theory.

Inclusion of B-fields leads to twisted K-groups.

D6-brane analyzed as a non-abelian monopole.

Abstract

In this review we show how K-theory classifies RR-charges in type II string theory and how the inclusion of the B-field modifies the general structure leading to the twisted K-groups. Our main purpose is to give an expository account of the physical relevance of K-theory and, in order to make it, we consider different points of view: processes of tachyon condensation, cancellation of global anomalies and gauge fixings. As a field to test the proposals of K-theory, we concentrate on the study of the D6-brane, now seen as a non-abelian monopole.