Perils of Towers in the Swamp: Dark Dimensions and the Robustness of Effective Field Theories

Recently there has been an interesting revival of the idea to use large extra dimensions to address the dark energy problem, exploiting the (true) observation that towers of states with masses split, by $M^2_N = f(N) m^2,$ with $f$ an unbounded function of the integer $N$, sometimes contribute to the vacuum energy only an amount of order $m^D$ in $D$ dimensions. It has been argued that this fact is a consequence of swampland conjectures and may require a departure from Effective Field Theory (EFT) reasoning. We test this claim with calculations for Casimir energies in extra dimensions. We show why the domain of validity for EFTs ensures that the tower spacing scale $m$ is always an upper bound on the UV scale for the lower-energy effective theory; use of an EFT with a cutoff part way up a tower is not a controlled approximation. We highlight the role played by the sometimes-suppressed contributions from towers in extra-dimensional approaches to the cosmological constant problem, old and new, and point out difficulties encountered in exploiting it. We compare recent swampland realizations of these arguments with earlier approaches using standard EFT examples, discussing successes and limitations of both.