Open string models with Scherk-Schwarz SUSY breaking and localized anomalies

We study examples of chiral four-dimensional IIB orientifolds with Scherk-Schwarz supersymmetry breaking, based on freely acting orbifolds. We construct a new Z_3 x Z_3' model, containing only D9-branes, and rederive from a more geometric perspective the known Z_6' x Z_2' model, containing D9, D5 and \bar D 5 branes. The cancellation of anomalies in these models is then studied locally in the internal space. These are found to cancel through an interesting generalization of the Green-Schwarz mechanism involving twisted Ramond-Ramond axions and four-forms. The effect of the latter amounts to local counterterms from a low-energy effective field theory point of view.