The effective action of type II Calabi‐Yau orientifolds

This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi‐Yau orientifolds in the presence of background fluxes by using a Kaluza‐Klein reduction. The Kähler potential, the gauge kinetic functions and the flux‐induced superpotential are determined in terms of geometrical data of the Calabi‐Yau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin's generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear multiplets makes contact to the underlying N = 2 special geometry. In type IIB setups, the flux‐potentials can be expressed in terms of superpotentials, D‐terms and, generically, a massive linear multiplet. The type IIA superpotential depends on all geometric moduli of the theory. It is reviewed, how type IIA orientifolds arise as a special limit of M‐theory compactified on specific G 2 manifolds by matching the effective actions. In a similar spirit type IIB orientifolds are shown to descend from F‐theory on a specific class of Calabi‐Yau fourfolds. In addition, mirror symmetry for Calabi‐Yau orientifolds is briefly discussed and it is shown that the N = 1 chiral coordinates linearize the appropriate instanton actions.