Towards a String Realization of the Dark Dimension via T-folds

In this work, we explore the feasibility of realizing the Dark Dimension Scenario through T-fold compactifications on $T^5\times S^1$, where the base of the internal space $S^1$ naturally acts as the requisite mesoscopic extra dimension. Utilizing Scherk–Schwarz reduction from 5D to 4D, and applying duality twists from both elliptic and parabolic conjugacy classes of subgroups of the T-duality group associated with $T^5$, we stabilize the volume of $T^5$ and several other moduli. This approach generates a potential characterized by two runaway directions, one aligned with the Scherk–Schwarz radion. Further stabilization efforts yield a decreasing potential trajectory demanded by the Dark Dimension Scenario.