Moduli Stabilisation for ADD and the Dark Dimension Scenario

Abstract

We provide a moduli stabilisation mechanism for realising anisotropic string compactifications with one or two large extra dimensions, corresponding to the ADD and Dark Dimension scenarios. This is achieved within the type IIB Large Volume Scenario, where an exponentially large Calabi-Yau volume in string units can naturally generate a parametrically low Kaluza-Klein scale. Anisotropy is realised by considering a Calabi-Yau threefold which is a K3 fibration over a $\mathbb{P}^1$ base. The volume of the 4D K3 fibre is stabilised at relatively small values by perturbative corrections to the effective action, in particular string loops and higher-derivative effects, leaving an exponentially large volume of the 2D $\mathbb{P}^1$ base. We argue that complex structure moduli stabilisation can dynamically deform the $\mathbb{P}^1$ base, corresponding to a Tyurin degeneration limit where the internal geometry effectively develops a single large 1D cycle. Within a unified description, the ADD case is instead recovered as a symmetric alternative limit. The potential can feature either a dS vacuum or a quintessence runaway, although in both cases some degree of tuning is required to match the observed cosmological constant scale. We also present an explicit Calabi-Yau orientifold example with consistent brane setup, tadpole cancellation and moduli stabilisation. We analyse the resulting moduli spectrum and associated phenomenological constraints, including supersymmetry breaking, cosmological moduli overproduction and fifth force bounds.