Mass Hierarchies and Quantum Gravity Constraints in DKMM-refined KKLT

We carefully revisit the mass hierarchies for the KKLT scenario with an uplift term from an anti D3-brane in a strongly warped throat. First, we derive the bound resulting from what is usually termed "the throat fitting into the bulk" directly from the Klebanov-Strassler geometry. Generating the small value of the superpotential $W_{0}$ via the mechanism proposed by Demirtas, Kim, McAllister and Moritz (DKMM), we identify two possible DKMM-refined KKLT scenarios for stabilizing the light axio-dilaton modulus. The first scenario spoils the expected hierarchy between the bulk and the throat mass scales and implies that the energy scale of the uplift is larger than the species scale of the effective theory in the throat. Moreover it requires an unnaturally large tadpole $N\sim 10^{7-8}$ that is certainly in conflict with tadpole cancellation. For the less restricted second scenario, the hierarchy can be controlled at the expense of, under the most optimistic assumptions, an only moderately large tadpole $N\sim 10^{2-3}$.