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

TL;DR

This work refines the KKLT moduli-stabilization program by preserving the dilaton and Kähler moduli couplings within a G-function framework, rather than integrating out all complex structure moduli holomorphically. Focusing on the elliptic Calabi–Yau X = P_{11169}[18] with its orientifold limit, the authors derive explicit W_flux and Kähler data in a two-parameter subspace, then construct an effective non-holomorphic W_eff(τ, T) that governs the remaining stabilization. Through careful analysis of the SUSY conditions for τ and the Kähler moduli across several flux cases, they demonstrate that in the main Case II (g≠0, h=0) there are no supersymmetric vacua, illustrating the necessity of their modified procedure. The results establish a concrete, analytically tractable framework for moduli stabilization beyond the conventional KKLT decoupling and pave the way for exploring more general fluxes and potential uplift mechanisms within explicit Calabi–Yau orientifolds.

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 Kähler 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.