Running decompactification, sliding towers, and the distance conjecture

We study towers of light particles that appear in infinite-distance limits of moduli spaces of 9-dimensional N= 1 string theories, some of which notably feature decompactification limits with running string coupling. The lightest tower in such decompactification limits consists of the non-BPS Kaluza-Klein modes of Type I ' string theory, whose masses depend nontrivially on the moduli of the theory. We work out the moduli-dependence by explicit computation, finding that despite the running decompactification the Distance Conjecture remains satisfied with an exponential decay rate alpha >= 1/root d - 2 in accordance with the sharpened Distance Conjecture. The related sharpened Convex Hull Scalar Weak Gravity Conjecture also passes stringent tests. Our results non-trivially test the Emergent String Conjecture, while highlighting the important subtlety that decompactifcation can lead to a running solution rather than to a higher-dimensional vacuum.