Abstract
We derive and generalize the RR twisted tadpole cancellation conditions necessary to obtain consistent D=4, ZNorbifold compactifications of Type IIB string theory. At least two different types of branes (or antibranes with opposite RR charges) are introduced into the construction. The matter spectra and their contribution to the non-Abelian gauge anomalies are computed. Their relation with the tadpole cancellation conditions is also reviewed. The presence of tachyons is a common feature for some of the nonsupersymmetric systems of branes.
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