Spectral morphisms, K-theory, and stable ranks

We give a brief account of the interplay between spectral morphisms, K-theory, and stable ranks in the context of Banach algebras.Comment: 12 pages; to appear in the Proceedings of the Workshop on Noncommutative Geometry (Fields Institute, Toronto 2008

String instantons, fluxes and moduli stabilization

We analyze a class of dual pairs of heterotic and type I models based on freely-acting $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifolds in four dimensions. Using the adiabatic argument, it is possible to calculate non-perturbative contributions to the gauge coupling threshold corrections on the type I side by exploiting perturbative calculations on the heterotic side, without the drawbacks due to twisted moduli. The instanton effects can then be combined with closed-string fluxes to stabilize most of the moduli fields of the internal manifold, and also the dilaton, in a racetrack realization of the type I model.Comment: 1+49 page

The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-Branes

In this paper, we work out in detail the tadpole cancellation conditions as well as the generalized Green-Schwarz mechanism for type IIB orientifold compactifications with D3- and D7-branes. We find that not only the well-known D3- and D7-tadpole conditions have to be satisfied, but in general also the vanishing of the induced D5-brane charges leads to a non-trivial constraint. In fact, for the case $h^{1,1}_{-} \neq 0$ the latter condition is important for the cancellation of chiral anomalies. We also extend our analysis by including D9- as well as D5-branes and determine the rules for computing the chiral spectrum of the combined system.Comment: 33+7 pages; 2 figures; v2: references added; v3: published versio