KKLT type models with moduli-mixing superpotential

TL;DR

The paper extends KKLT constructions by introducing moduli mixing in the gauge kinetic function, with one modulus stabilized by flux while a nonperturbative term from gluino condensation stabilizes the Kähler modulus $T$ without heavy flux tuning. Four explicit models explore how different moduli mixings and brane setups modify the SUSY-breaking pattern, quantified by the parameter $ ext{alpha}$ that governs the balance between modulus mediation and anomaly mediation. Some models (notably 2 and 4) exhibit dominant anomaly mediation, while others (1 and 3) allow sizable modulus contributions, yielding rich soft spectra; Be$^{bT}$-type nonperturbative terms in Models 3 and 4 also improve cosmological behavior, potentially avoiding overshoot and finite-temperature destabilization. The framework yields hierarchical scales via magnetic flux and suggests heavy gravitino/moduli scenarios compatible with cosmological constraints, motivating further phenomenological and cosmological analyses.

Abstract

We study KKLT type models with moduli-mixing superpotential. In several string models, gauge kinetic functions are written as linear combinations of two or more moduli fields. Their gluino condensation generates moduli-mixing superpotential. We assume one of moduli fields is frozen already around the string scale. It is found that Kähler modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on (non-)magnetized D-brane. Furthermore, we do not need to highly tune parameters in order to realize a weak gauge coupling and a large hierarchy between the gravitino mass and the Planck scale, when there exists non-perturbative effects on D3-brane. SUSY breaking patterns in our models have a rich structure. Also, some of our models have cosmologically important implications, e.g., on the overshooting problem and the destabilization problem due to finite temperature effects as well as the gravitino problem and the moduli problem.

Figures (2)

• Figure 1: A potential plot of KKLT model with parameters, $w_0=10^{-13}$, $C=N,~a=8\pi^2/N$, $N=5$ and $D=6.3\times 10^{-27}$. Then, we obtain $\langle ReT \rangle \simeq 2.2$ and $m_{3/2} \simeq 25$ TeV. A horizontal axis is $t=ReT$ and a vertical axis is $V$.
• Figure 2: The potential of model 4 with parameters, $n_T=3,~n_S=1,~ n_p=2$, $N_a=4,~ N_b=5,~ m_b=6,~ w_b= 3,~\langle ReS \rangle =1,~ D= 2.2 \times 10^{-27}$. Then, we obtain $\langle ReT \rangle \simeq 1.4$, $M_{string}/M_p \simeq 0.22$ and $m_{3/2} \simeq 40$ TeV. A horizontal axis is $t=ReT$ and a vertical axis is $\ln[V]$. This potential can make sense until $ReT < m_b \langle ReS \rangle /w_b = 2$.