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.

We consider α′2 curvature corrections to the action of an NS5-brane which plays the key role in the metastability analysis of warped anti-D3-brane uplifts by Kachru, Pearson and Verlinde (KPV). Such corrections can dramatically alter the KPV analysis. We find that for the α′2-corrections to be sufficiently small to recover essentially the leading-order KPV potential one needs a surprisingly large S3 radius, corresponding to gsM > 20. In the context of the Large Volume Scenario (LVS) this implies a D3-tadpole of at least (103–104). However, large α′2-corrections do not necessarily spoil the uplift in KPV. Rather, as the curvature corrections lower the tension of the brane, a novel uplifting mechanism suggests itself where the smallness of the uplift is achieved by a tuning of curvature corrections. A key underlying assumption is the existence of a dense discretuum of gs. This new mechanism does not require a deep warped throat, thereby sidestepping the main difficulty in uplifting KKLT and LVS. However, all of the above has to be treated as a preliminary exploration of possibilities since, at the moment, not all relevant corrections at the order α′2 are known.

To establish metastable de Sitter vacua or even just scale-separated AdS, control over perturbative corrections to the string-derived leading-order 4d lagrangian is crucial. Such corrections can be classified in three types: first, there are genuine loop effects, insensitive to the UV completion of the 10d theory. Second, there are local α′ corrections or, equivalently, 10d higher-dimension operators which may or may not be related to loop-effects. Third, warping corrections affect the 4d Kahler potential but are expected not to violate the 4d no-scale structure. With this classification in mind, we attempt to derive the Berg-Haack-Pajer conjecture for Kahler corrections in type-IIB Calabi-Yau orientifolds and extend it to include further terms. This is crucial since the interesting applications of this conjecture are in the context of generic Calabi-Yau geometries rather than in the torus-based models from which the main motivation originally stems. As an important by-product, we resolve a known apparent inconsistency between the parametric behaviour of string loop results and field-theoretic expectations. Our findings lead to some interesting new statements concerning loop effects associated with blowup-cycles, loop corrections in fibre inflation, and possible logarithmic effects in the Kahler and scalar potential.