The LVS Parametric Tadpole Constraint

The large volume scenario (LVS) for de Sitter compactifications of the type IIB string is, at least in principle, well protected from various unknown corrections. The reason is that, by construction, the Calabi-Yau volume is exponentially large. However, as has recently been emphasised, in practice the most explicit models are rather on the border of parametric control. We identify and quantify parametrically what we believe to be the main issue behind this difficulty. Namely, a large volume implies a shallow AdS minimum and hence a small uplift. The latter, if it relies on an anti-D3 in a throat, requires a large negative tadpole. As our main result, we provide a simple and explicit formula for what this tadpole has to be in order to control the most dangerous corrections. The fundamental ingredients are parameters specifying the desired quality of control. We comment on the interplay between our constraint and the tadpole conjecture. We also discuss directions for future work which could lead to LVS constructions satisfying the tadpole constraint with better control, as well as further challenges that may exist for the LVS. Our formula then represents a very concrete challenge for future searches for and the understanding of relevant geometries.