Topics on D-brane charges with B-fields

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.Comment: 63 pages, no figures. To appear in the special issue of Int. J. Geom. Meth. Mod. Phys., v.1, N4 (August 2004

Non-holomorphic Corrections from Threebranes in F Theory

We construct solutions of type IIB supergravity dual to N=2 super Yang-Mills theories. By considering a probe moving in a background with constant coupling and an AdS_{5} component in its geometry, we are able to reproduce the exact low energy effective action for the theory with gauge group SU(2) and N_{f}=4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS_{5} geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. By considering a Wilson loop in this geometry we are also able to compute the instanton effects on the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action are in complete agreement with field theory expectations.Comment: 23 pages, uses harvmac, References added, typos corrected and minor improvements to discussion of N dependence, to appear in Phys. Rev.