On the modified KKLT procedure:: A case study for the P11169[18] model

We probe the existence of supersymmetric vacua of the type 1113 orientifold of the elliptic Calabi-Yau space P-11169[18] where generically two complex structure moduli Z(i), the dilaton tau and the two Kahler moduli T-i are stabilized by fluxes and gaugino condensates. The usual KKLT procedure, which integrates out the complex structure moduli and the dilaton, actually has to be modified, such that one keeps the dependence on tau. We derive explicitly the resulting effective superpotential W-eff(tau) for the dilaton for various flux combinations. As this is actually a nonholomorphic quantity one must properly work with the G-function. The remaining SUSY equations for tau and the T-i can be resolved explicitly.