On the modified KKLT procedure: a case study for the P_{11169}[18] model

TL;DR

This paper investigates the stabilization of moduli in a specific type IIB string compactification, revealing that the standard KKLT procedure must be modified to retain dilaton dependence, and provides explicit solutions for the effective superpotential.

Contribution

It demonstrates a necessary modification to the KKLT procedure for the P_{11169}[18] model, deriving explicit effective superpotentials that account for dilaton dependence.

Findings

Modified KKLT procedure retains dilaton dependence.

Explicit effective superpotential W_{eff}(tau) derived.

Supersymmetric vacua solutions explicitly obtained.

Abstract

We probe the existence of supersymmetric vacua of the type IIB orientifold of the elliptic Calabi-Yau space P_{11169}[18] where generically two complex structure moduli z_i, the dilaton tau and the two K\"ahler 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 explicitely the resulting effective superpotential W_{eff}(tau) for the dilaton for various flux combinations. As this is actually a non-holomorphic quantity one must properly work with the G-function. The remaining SUSY equations for tau and the T_i can be resolved explicitely.