Supersymmetry and Stability of Flux Vacua

TL;DR

This work addresses moduli stabilization in type IIB string theory by constructing a supersymmetric Minkowski vacuum using a racetrack nonperturbative superpotential together with flux stabilization, ensuring $W=0$ and $DW=0$ for all moduli and a positive moduli mass matrix. By solving these conditions for $ au$, complex-structure moduli, and the volume modulus, they stabilize the volume at a finite $\rho_0$ prior to uplifting. A concrete example shows a stable minimum with the volume modulus at $\rho_0\approx 95$, while highlighting how the complex-structure Kähler potential can suppress the effective scale of the potential via $e^{K}$. The results offer a robust route to vacuum stability in the string landscape and a framework for exploring nonperturbative corrections beyond the original KKLT setup.

Abstract

We describe a modified KKLT mechanism of moduli stabilization in a supersymmetric Minkowski vacuum state. In this mechanism, supersymmetry ensures vacuum stability and positivity of the mass matrix for the dilaton, complex structure, and the volume modulus.

Figures (1)

• Figure 1: Potential of the volume modulus for $a ={2\pi\over 200}$, $b ={2\pi\over 100}$, $A = - \beta$, $B = 10 \beta,$ where $\beta = 3.06 - 7.39 \, i$. The potential is shown in units of $10^{-15}M^{4}_{p}$.