O'KKLT

TL;DR

The paper addresses the challenge of stabilizing all moduli in a de Sitter vacuum while controlling the gravitino mass within string-inspired constructions. It introduces O'KKLT, a fusion of a quantum-corrected O'Raifeartaigh sector with KKLT moduli stabilization, providing an uplift mechanism that yields a dS minimum and stabilized moduli. The authors show that the minimum remains near the origin for the O'Raifeartaigh sector, with $|S| \approx \frac{\sqrt{3}}{6}\Lambda^2$ and $m_{3/2} \approx \frac{\mu^4}{3(2\sigma_0)^3}$, and that TeV-scale gravitino masses are attainable under consistent parameter choices. Extending to KL racetrack models, they demonstrate that the gravitino mass can be made extremely small while maintaining a large stabilization barrier, enabling high-scale inflation ($H \gg m_{3/2}$) and vacuum stability. The work thus provides a concrete framework for F-term uplifting with dynamical SUSY breaking in string-inspired cosmology, offering a route to light gravitino scenarios compatible with cosmological evolution.

Abstract

We propose to combine the quantum corrected O'Raifeartaigh model, which has a dS minimum near the origin of the moduli space, with the KKLT model with an AdS minimum. The combined effective N=1 supergravity model, which we call O'KKLT, has a dS minimum with all moduli stabilized. Gravitino in the O'KKLT model tends to be light in the regime of validity of our approximations. We show how one can construct models with a light gravitino and a high barrier protecting vacuum stability during the cosmological evolution.

Figures (4)

• Figure 1: The slice of the O'KKLT potential at vanishing axions $y$ and $\alpha$, multiplied by $10^{31}$, for the values of the parameters $A=1,~a=0.25,~W_0= - 10^{-12},~\mu^2=1.66\times 10^{-12},~L=10^{-3}$. The potential has a dS minimum at $\sigma\approx 123$, $x\sim 3 \cdot 10^{-7}$. The gravitino mass in this example is $m_{3/2} \sim 600$ GeV.
• Figure 2: The lowest curve with dS minimum is the one from the uplifted KKLT model. The second one describes the inflationary potential with the term $V_{\rm infl}={V(\phi)\over \sigma^3}$ added to the KKLT potential. The top curve shows that when the inflationary potential becomes too large, the barrier disappears, and the internal space decompactifies. This explains the constraint $H\lesssim m_{3/2}$.
• Figure 3: The KL potential multiplied by $10^{14}$, with the parameters $A=1,\ B=-1.03,\ a=2\pi/100,\ b=2\pi/99,\ W_0= - 2\times 10^{-4}$. The first minimum, corresponding to the supersymmetric Minkowski vacuum, stabilizes the volume at $\sigma\approx 62$. If one slightly changes the parameters (e.g. takes $B = 1.032$), this minimum shifts down, and becomes a very shallow AdS minimum, see the thin black line in Fig. \ref{['plot2']}.
• Figure 4: The thin black line shows the potential in the KL model, multiplied by $10^{14}$, for the values of the parameters $A=1,\ B=-1.032,\ a=2\pi/100,\ b=2\pi/99,\ W_0= - 2\times 10^{-4}$. The shallow AdS minimum (almost Minkowski) stabilizes the volume at $\sigma\approx 67$. The thick blue line shows the potential after the O'Raifeartaigh uplifting with $\mu^2=0.66 \times 10^{-4}$, $L=10^{-3}$. The AdS minimum after the uplifting becomes a (nearly Minkowski) dS minimum.