Moduli stabilization in type IIB orientifolds (II)

We discuss general properties of moduli stabilization in KKLT scenarios in type IIB orientifold compactifications X6X6. In particular, we find conditions for the Kähler potential to allow a KKLT scenario for a manifold X6X6 without complex structure moduli, i.e. h(2,1)(−)(X6)=0. This way, a whole class of type IIB orientifolds with h(2,1)(−)(X6)=0 is ruled out. This excludes in particular all ZNZN- and ZN×ZMZN×ZM-orientifolds X6X6 with h(2,1)(X6)=0h(2,1)(X6)=0 for a KKLT scenario. This concerns Z3Z3, Z7Z7, Z3×Z3Z3×Z3, Z4×Z4Z4×Z4, Z6×Z6Z6×Z6 and Z2×Z6′Z2×Z6′-both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kähler moduli associated to the odd cohomology H−(1,1)(X6). In the second part of this work we discuss the moduli stabilization of resolved type IIB ZNZN- or ZN×ZMZN×ZM-orbifold/orientifold compactifications. As examples for the resolved Z6Z6 and Z2×Z4Z2×Z4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.