Dilaton stabilization in KKLT revisited

TL;DR

This paper revisits the conditions for dilaton stabilization in KKLT-type flux compactifications, highlighting potential instabilities due to mass mixing and flux configurations, and clarifying the necessary flux conditions for stable solutions.

Contribution

It provides a detailed analysis of dilaton stabilization conditions in KKLT scenarios, identifying when saddle points and instabilities occur, and clarifies the flux conditions needed for stability.

Findings

Dilaton mass is linked to gravitino mass and complex structure moduli stabilization.

Saddle point instability arises when dilaton mass is not significantly enhanced.

Stable stabilization requires specific NS 3-form flux configurations.

Abstract

We study the condition for the dilaton stabilization in Type IIB flux compactifications consistent with the KKLT scenario. Since the Gukov-Vafa-Witten superpotential depends linearly on the dilaton, the dilaton mass squared is given by a sum of the gravitino mass squared and additional terms determined by the complex structure moduli stabilization. If the dilaton mass is not much enhanced from the gravitino mass, the mass mixing with the K\"ahler modulus in the presence of the non-perturbative effect generates the saddle point at the supersymmetric field values, hence the potential becomes unstable. When the complex structure moduli other than the conifold modulus are neglected, the saddle point problem arises over the controllable parameter space. We also point out that the dilaton stabilization condition is equivalent to the condition on the NS 3-form fluxes, $|H_{(1,2)}| > | H_{(0,3)}|$.