Moduli Stabilisation for Chiral Global Models

TL;DR

This work tackles simultaneous moduli stabilisation and global chiral model building in Type IIB/F-theory on toric Calabi–Yau orientifolds. It develops a framework where $S$ and $U$ are fixed at tree level while Kaehler moduli are stabilised through a combination of non-perturbative effects on a diagonal del Pezzo plus $\alpha'$ and string-loop corrections, all within the Kaehler cone. By constructing explicit global models on a K3-fibred Calabi–Yau with four Kaehler moduli, the authors realize LVS-like vacua that yield GUT- or MSSM-like spectra with TeV-scale SUSY or large volumes, and they demonstrate how to preserve chirality while avoiding Freed-Witten and D-term obstructions. The results provide concrete, globally consistent realizations of LVS in chiral compactifications, with clear phenomenological scales and promising cosmological implications, and they lay out several avenues for further development, including flux stabilisation of complex structure and inflationary dynamics.

Abstract

We combine moduli stabilisation and (chiral) model building in a fully consistent global set-up in Type IIB/F-theory. We consider compactifications on Calabi-Yau orientifolds which admit an explicit description in terms of toric geometry. We build globally consistent compactifications with tadpole and Freed-Witten anomaly cancellation by choosing appropriate brane set-ups and world-volume fluxes which also give rise to SU(5)- or MSSM-like chiral models. We fix all the Kaehler moduli within the Kaehler cone and the regime of validity of the 4D effective field theory. This is achieved in a way compatible with the local presence of chirality. The hidden sector generating the non-perturbative effects is placed on a del Pezzo divisor that does not have any chiral intersections with any other brane. In general, the vanishing D-term condition implies the shrinking of the rigid divisor supporting the visible sector. However, we avoid this problem by generating r<n D-term conditions on a set of n intersecting divisors. The remaining (n-r) flat directions are fixed by perturbative corrections to the Kaehler potential. We illustrate our general claims in an explicit example. We consider a K3-fibred Calabi-Yau with four Kaehler moduli, that is an hypersurface in a toric ambient space and admits a simple F-theory up-lift. We present explicit choices of brane set-ups and fluxes which lead to three different phenomenological scenarios: the first with GUT-scale strings and TeV-scale SUSY by fine-tuning the background fluxes; the second with an exponentially large value of the volume and TeV-scale SUSY without fine-tuning the background fluxes; and the third with a very anisotropic configuration that leads to TeV-scale strings and two micron-sized extra dimensions. The K3 fibration structure of the Calabi-Yau three-fold is also particularly suitable for cosmological purposes.

Figures (2)

• Figure 1: Plot of $\ln(V)$ as a function of ${\cal{V}}$ and $\tau_7$. In the region where the logarithm is undefined the potential becomes negative and develops a global minimum whose presence is guaranteed by the fact that $V\to 0$ at infinite volume.
• Figure 2: The potential for $\tau_s$ at fixed ${\cal{V}}$, $\tau_4$ and $\tau_7$ (we rescaled $V\to {\cal{V}}^3 \cdot V$). The plot shows also how the minimum lies within the Kähler cone since the most constraining condition $r_2>0$ corresponds to $\tau_s>\tau_7$ (combined with $\sqrt{\tau_7}=- t_1 >0$ and $\sqrt{\tau_s}= t_2+t_4>0$ which is obtained from the condition $r_3>0$ after using the D-term constraint).