Magnetized four-dimensional Z2 x Z2 orientifolds

We study deformations of Z(2) x Z(2) (shift-)orientifolds in four dimensions in the presence of both uniform Abelian internal magnetic fields and quantized NS-NS B-ab backgrounds, that are shown to be equivalent to asymmetric shift-orbifold projections. These models are related by T-duality to orientifolds with D-branes intersecting at angles. As in corresponding six-dimensional examples, D9-branes magnetized along two internal directions acquire a charge with respect to the R-R sixform, contributing to the tadpole of the orthogonal D5-branes ("brane transmutation"). The resulting models exhibit rank reduction of the gauge group and multiple matter families, due both to the quantized B-ab and to the background magnetic fields. Moreover, the low-energy spectra are chiral and anomaly free if additional D5-branes longitudinal to the magnetized directions are present, and if there are no Ramond-Ramond tadpoles in the corresponding twisted sectors of the undeformed models. (C) 2003 Elsevier B.V. All rights reserved.