Type IIB orientifolds with NS-NS antisymmetric tensor backgrounds

We consider six dimensional N=1 space-time supersymmetric type IIB orientifolds with a nonzero untwisted NS-NS sector B field. The B field is quantized due to the requirement that the type IIB spectrum be left-right symmetric. The presence of the B field results in rank reduction of both 99 and 55 open string sector gauge groups. We point out that in some of the models with a nonzero B field there are extra tensor multiplets in the Z₂ twisted closed string sector, and we explain their origin in a simple example. Also, the 59 open string sector states come with a multiplicity that depends on the B field. These two facts are in accord with anomaly cancellation requirements. We point out relations between various orientifolds with and without the B field, and also discuss the F-theory duals of these models.