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 $\rho$, that is obtained from swampland conjectures in string theory, is confronted with the corresponding result for $\rho$ in the effective field theory (EFT) limit. One of the problems concerns the widely spread belief that in higher dimensional EFTs with compact dimensions the vacuum energy is automatically finite. On the contrary, our analysis shows that $\rho$ contains (previously missed) UV-sensitive terms. Our work was challenged in [3]. Here we show why in our opinion the claims in [3] are flawed, and provide further support to our findings. We conclude presenting ideas on the physical mechanism that should dispose of the large UV contributions to $\rho$.