Chiral global embedding of Fibre Inflation with $\overline{\rm D3}$ uplift

Abstract: We carefully analyse the challenges posed by the construction of type IIB chiral global embeddings of Fibre Inflation with $\overline{ \rm D3}$ uplift to a de Sitter vacuum. We present an explicit example involving an $h^{1,1}=4$ Calabi-Yau manifold with a K3 fibration and a del Pezzo divisor supporting non-perturbative effects. The chosen orientifold involution induces O3-planes that can be placed on top of each other at the tip of the throat of a deformed conifold singularity. The D7-brane sector contains standard magnetised branes and a Whitney brane. The former induce chiral matter and generate quantum effects that stabilise the K\"ahler moduli, while the latter helps to increase the total D3-charge. We study in detail the constraints on the parameter space leading to an observationally viable inflationary dynamics, finding several regions where the effective field theory is under control.