Tadpole versus anomaly cancellation in D = 4,6 compact IIB orientifolds

It is often stated in the literature concerning D=4,6 compact Type IIBorientifolds that tadpole cancellation conditions i) uniquely fix the gaugegroup (up to Wilson lines and/or moving of branes) and ii) are equivalent togauge anomaly cancellation. We study the relationship between tadpole andanomaly cancellation conditions and qualify both statements. In general thetadpole cancellation conditions imply gauge anomaly cancellation but arestronger than the latter conditions in D=4, N=1 orientifolds. We also find thattadpole cancellation conditions in Z_N D=4,6 compact orientifolds do notcompletely fix the gauge group and we provide new solutions different fromthose previously reported in the literature.Comment: 28 pages, Latex. Minor corrections, updated reference