Topological constraints in the LARGE-volume scenario

Abstract

Abstract We elaborate on recent results regarding the self-consistency of de Sitter vacua in the LARGE-volume scenario of type IIB string theory. In particular, we analyze to what extent the control over warping, curvature and gs corrections depends on the topology and the orientifold/brane data of a compactification. We compute a general bound on the magnitude of these corrections which strongly constrains the D3 tadpole. The minimally required tadpole ranges from $$ \mathcal{O} $$ O (500) to $$ \mathcal{O} $$ O (106) or more and depends strongly on other data, in particular on the Euler number of the Calabi-Yau 3-fold, the triple-self-intersection and Euler numbers of the small divisor and the coefficient as appearing in the non-perturbative superpotential. We give arguments suggesting that satisfying these constraints is very challenging and perhaps impossible.