Topological constraints in the LARGE-volume scenario

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 g(s) 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 O(500) to O(10(6)) 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 a(s) appearing in the non-perturbative superpotential. We give arguments suggesting that satisfying these constraints is very challenging and perhaps impossible.

Automated summary

In this article, we elaborate on the self-consistency of de Sitter vacua in the LARGE-volume scenario of type IIB string theory. We analyze the control over warping, curvature, and g(s) corrections, which depend on the compactification's topology and orientifold/brane data. By computing a general bound on the magnitude of these corrections, we find that the D3 tadpole is strongly constrained. The required tadpole ranges from O(500) to O(10(6)) or more, depending on factors such as the Euler number of the Calabi-Yau 3-fold, the triple-self-intersection and Euler numbers of the small divisor, and the coefficient a(s) in the non-perturbative superpotential.