Moduli stabilization in type IIB orientifolds (II)

Abstract

We discuss general properties of moduli stabilization in KKLT scenarios in type IIB orientifold compactifications X 6 . In particular, we find conditions for the Kähler potential to allow a KKLT scenario for a manifold X 6 without complex structure moduli, i.e. h ( 2 , 1 ) ( − ) ( X 6 ) = 0 . This way, a whole class of type IIB orientifolds with h ( 2 , 1 ) ( − ) ( X 6 ) = 0 is ruled out. This excludes in particular all Z N - and Z N × Z M -orientifolds X 6 with h ( 2 , 1 ) ( X 6 ) = 0 for a KKLT scenario. This concerns Z 3 , Z 7 , Z 3 × Z 3 , Z 4 × Z 4 , Z 6 × Z 6 and Z 2 × Z 6 ′ -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 ) ( X 6 ) . In the second part of this work we discuss the moduli stabilization of resolved type IIB Z N - or Z N × Z M -orbifold/orientifold compactifications. As examples for the resolved Z 6 and Z 2 × Z 4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.