Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter

TL;DR

The paper tackles explicit stabilization of all closed-string moduli in fluxed Type IIB Calabi–Yau compactifications with chiral matter. It combines toric CY constructions with del Pezzo singularities and Greene–Plesser symmetries to reduce the complex-structure sector, enabling explicit flux vacua computation via periods and the prepotential, followed by LVS-like stabilisation of Kähler moduli using D-terms, non-perturbative and α′ corrections. The authors realize AdS and de Sitter minima with a realistic visible sector located at a shrinking dP_6 singularity that can Higgs to dP_3, achieving controlled hierarchies and soft terms in a sequestered scenario. This work demonstrates a concrete path to fully explicit, phenomenologically viable string vacua with stabilized moduli and chiral matter, offering a framework for further exploration of inflation and vacuum statistics in the string landscape.

Abstract

We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kaehler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kaehler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative alpha'-corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP_6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP_3 singularity.

Figures (5)

• Figure 1: From left to right, the quiver diagram, the toric diagram and the dimer diagram for the $\mathbb{C}^3/\mathbb{Z}_3\times\mathbb{Z}_3$ orbifold singularity.
• Figure 2: After assigning VEVs for the fields $X_{14},$$Y_{58}$, $Z_{73}$ the matter content shown in the quiver diagram on the left side remains. The resulting dimer after the higgsing is shown on the right side. The remaining gauge theory is that of dP$_3$.
• Figure 3: Distribution of flux solutions in the $(g_s,|W_0|)$-plane in the fundamental domain after performing appropriate $SL(2,\mathbb{Z})$ transformations.
• Figure 4: Distribution of solutions in the fundamental domain of $\tau,$ i.e. in the $(\text{Re}[\tau],\text{Im}[\tau]=1/g_s)$ plane (top left). Next to it (top right) we show the distribution in the $(\text{Re}[\tau],1/\text{Im}[\tau]=g_s)$ plane. The bottom shows the distribution of minima with respect to values of $g_s$ before restricting to small instanton corrections. Gray points correspond to points with large instanton corrections, blue and red points correspond to small instanton contributions taking corrections up to order 2 and 10 into account.
• Figure 5: The same distributions as before but for $\mathbb{P}_{1,1,1,6,9}.$ Distribution of solutions in the fundamental domain of $\tau,$ i.e. in the $(\text{Re}[\tau],\text{Im}[\tau]=1/g_s)$ plane (top). In the middle we show the distribution in the $(\text{Re}[\tau],1/\text{Im}[\tau]=g_s)$ plane. The bottom shows the distribution of minima with respect to values of $g_S$ before restricting to small instanton corrections. Gray points correspond to points with large instanton corrections, blue and red points correspond to small instanton contributions taking corrections up to order 2 and 14 into account (again requiring $|F_{\rm inst}|/|F|<0.1$ and ${\rm max}_i\left(|F^i_{\rm inst}|\right)/|F|<0.1$).