Sigma-model anomalies in compact D=4, N=1 Type IIB orientifolds and Fayet-Iliopoulos terms

Compact Type IIB D=4, N=1 orientifolds have certain U(1) σ-model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of ZN orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singularities and it requires the mixing between twisted and untwisted moduli of the orbifold. As a consequence, the Fayet-Iliopoulos terms which are present for the gauged anomalous U(1)'s of the models get an additional untwisted modulus dependent piece at the tree level