Dark Dimension and the Effective Field Theory limit

In [1] we pointed out that in the Dark Dimension scenario [2] theoretical issues arise when the prediction for the vacuum energy ρ, that is obtained from swampland conjectures in string theory, is confronted with the corresponding result for ρ in the field theory limit. One of the problems arises from the field theory side and is due to previous results for ρ that, according to our analysis, turn out to be incorrect, although widely spread. Our work was challenged in [3]. Here we show why in our opinion the claims in [3] are inconsistent, actually based on arguments deprived of physical meaning, providing further support to our findings. We conclude by discussing ideas on the physical mechanism that could trigger the suppression of large UV contributions to ρ.