Chiral Global Embedding of Fibre Inflation Models

TL;DR

This work addresses the challenge of embedding fibre inflation in a globally consistent type IIB string compactification with a chiral visible sector. It constructs an explicit h^{1,1}=4 Calabi–Yau with three K3 fibrations and a diagonal del Pezzo divisor, implements D-term stabilisation to reduce to the fibre-inflation setup, and derives the inflationary potential from string loop and higher-derivative corrections. Through both single-field and multi-field analyses, the study reveals stringent constraints from the Kähler cone on the inflaton range and demonstrates viable regions (e.g., N_e ≈ 52, r ≈ 0.001–0.01) under specific parameter choices, while also showing cases requiring additional mechanisms (such as curvatons) to generate density perturbations. The results mark a significant step toward robust, globally consistent fibre inflation models with chirality, while outlining essential future work on uplifting, perturbative corrections, and a precise Calabi–Yau Kähler cone determination.

Abstract

We construct explicit examples of fibre inflation models which are globally embedded in type IIB orientifolds with chiral matter on D7-branes and full closed string moduli stabilisation. The minimal setup involves a Calabi-Yau threefold with h^{1,1}=4 Kaehler moduli which features multiple K3 fibrations and a del Pezzo divisor supporting non-perturbative effects. We perform a consistent choice of orientifold involution, brane setup and gauge fluxes which leads to chiral matter and a moduli-dependent Fayet-Iliopoulos term. After D-term stabilisation, the number of Kaehler moduli is effectively reduced to 3 and the internal volume reduces to the one of fibre inflation models. The inflationary potential is generated by suitable string loop corrections in combination with higher derivative effects. We analyse the inflationary dynamics both in the single-field approximation and by numerically deriving the full multi-field evolution in detail. Interestingly, we find that the Kaehler cone conditions set strong constraints on the allowed inflaton field range.

Figures (11)

• Figure 1: Plot of the inflationary potential for the example set (\ref{['ex_set_exA']}). The red vertical lines correspond to the walls of the Kähler cone while the dashed vertical lines denote horizon exit and the end of inflation where $\epsilon=1$.
• Figure 2: Comparison between the different KK masses, $m_{3/2}$ and the inflationary energy density $V^{1/4}$ from horizon exit to the end of inflation. Note that $M_{ \rm KK}^{(4)} = M_{ \rm KK}^{(6)}$ which is why only one of them is displayed here.
• Figure 3: Plot of the inflationary potential for the example set (\ref{['ex_set_exA2']}). The red vertical lines correspond to the walls of the Kähler cone while the dashed vertical lines denote horizon exit and the end of inflation where $\epsilon=1$.
• Figure 4: Comparison between the different KK masses, the gravitino mass $m_{3/2}$ and the inflationary energy $V^{1/4}$ from horizon exit to the end of inflation. Note that $M_{ \rm KK}^{(4)} = M_{ \rm KK}^{(6)}$ which is why only one of them is displayed here.
• Figure 5: Evolution of the $\epsilon$-parameter as a function of the number of efoldings $N$ for (left) the entire inflationary dynamics and (right) for the last efolding.