In the framework of type II super-string theory, there are two fundamental pictures that describe and classify D-brane charges and the Ramond-Ramond fields. The first one relies on classical cohomology. In particular, the Ramond-Ramond fields are classified by ordinary differential cohomology and the Wess-Zumino action turns out to be the holonomy of a differential cohomology class along the world-volume. The other fundamental classification scheme relies on K-theory. We will try to clarify how to correctly define the world-volume in this picture, in order to get a suitable generalization of the holonomy map to differential K-theory and to give a correct definition of the Wess-Zumino action. We will see that such a definition naturally leads to the notion of differential K-character and we will draw a complete parallel between the two classification schemes.

University of Sao Carlos (Brasil)