Type II flux compactifications

Orientifolds of type II string theory offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NSNS and RR field strengths, but also fluxes that are T-dual to the NSNS three-form flux. These additional ingredients can help stabilize moduli and lead to D-term contributions to the effective scalar potential. We describe in general how these fluxes appear as parameters of an effective N = 1 supergravity theory in four dimensions for type IIA and type IIB string theory. We also show how these fluxes arise from compactifications on six-dimensional spaces that can be described by toroidal fibers twisted over a toroidal base. This approach leads us to a more subtle treatment of the quantization of the general NSNS fluxes. We illustrate these phenomena with examples of certain orientifolds of T⁶/Z₄.