Uplift and towers of states in warped throat

Abstract

We investigate the connection between the distance conjecture and the uplift potential. For this purpose, we consider the concrete model, the warped deformed conifold embedded into Type IIB flux compactifications, with the uplift potential produced by $\overline{\rm D3}$-branes at the tip of the throat. Whereas the various mass scales associated with towers of states can be found, it turns out that the lightest tower mass scale satisfies the scaling behavior with respect to the uplift potential, which is meaningful provided the number of $\overline{\rm D3}$-branes is nonzero. This indicates that the effective theory becomes invalid in the vanishing limit of the uplift potential by the descent of an infinite tower of states from UV, as predicted in the distance conjecture. Since too large uplift potential is also problematic due to the runaway behavior of the moduli potential as well as the sizeable backreaction of $\overline{\rm D3}$-branes, the uplift potential is bounded from both above and below. In the simple model like the KKLT or the large volume scenario in which non-perturbative effect is dominatd by the single term, this bound can be rewritten as the bound on the size of the superpotential.