Type IIB Orientifolds without Untwisted Tadpoles, and non-BPS D-branes

We discuss the construction of six- and four-dimensional Type IIB orientifolds with vanishing untwisted RR tadpoles, but generically non-zero twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane systems with zero untwisted RR charge, but non-zero twisted RR charges. We construct explicit models containing branes and antibranes at fixed points of the internal space, or non-BPS branes partially wrapped on it. The models are non-supersymmetric, but are absolutely stable against decay to supersymmetric vacua. For particular values of the compactification radii tachyonic modes may develop, triggering phase transitions between the different types of non-BPS configurations of branes, which we study in detail in a particular example. As an interesting spin-off, we show that the $\IT^6/\IZ_4$ orientifold without vector structure, previously considered inconsistent due to uncancellable twisted tadpoles, can actually be made consistent by introducing a set of brane-antibrane pairs whose twisted charge cancels the problematic tadpole.