We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. Z k , the gauge couplings of U(1) gauge symmetries become weak in the limit of large k, as g → k −α with α a positive order 1 coefficient. The conjecture is based on black hole arguments combined with the Weak Gravity Conjecture (or the BPS bound in the supersymmetric setup), and the species bound. We provide explicit examples based on type IIB on AdS 5 × S 5 /Z k orbifolds, and M-theory on AdS 4 × S 7 /Z k ABJM orbifolds (and their type IIA reductions). We study AdS 4 vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete Z k symmetry for domain walls. We accordingly propose a refined version of the strong AdS Distance Conjecture, including a parametric dependence on the order of the discrete symmetry for 3-forms.

We show that warped throats of the Klebanov-Strassler kind, regarded as 5d flux compactifications on Sasaki-Einstein manifolds X 5 , describe fully backreacted solutions of transplanckian axion monodromy. We show that the asymptotic Klebanov-Tseytlin solution features a 5d axion physically rolling through its dependence on an spatial coordinate, and traversing arbitrarily large distances in field space. The solution includes the backreaction on the breathing mode of the compactification space and on the vacuum energy, which yields a novel form of flattening.We establish the description of the system in terms of an effective 5d theory for the axion, and verify its validity in transplanckian regimes. In this context, rolling axion monodromy configurations with limited field space range would correspond, in the holographic dual field theory, to duality walls, which admit no embedding in string theory so far. We present an identical realization of transplanckian axion monodromy in 4d in fluxed version of AdS 4 × X 7 . We speculate that similar models in which the axion rolls in the time direction naturally correspond to embedding the same mechanism in de Sitter vacua, thus providing a natural arena for large field inflation, and potentially linking the swampland de Sitter and distance conjectures. arXiv:1812.05016v3 [hep-th]