Running Decompactification, Sliding Towers, and the Distance Conjecture

TL;DR

This paper investigates towers of light particles in 9D string theories with decompactification limits, confirming the Distance Conjecture's exponential decay rate and testing the Emergent String Conjecture in scenarios with running couplings.

Contribution

It explicitly computes moduli-dependent masses of light towers in 9D string theories, demonstrating the Distance Conjecture holds even with running decompactification and testing the Emergent String Conjecture.

Findings

Distance Conjecture's exponential decay rate is satisfied with α ≥ 1/√(d-2)

The sharpened Convex Hull Scalar Weak Gravity Conjecture passes tests

Decompactification can lead to running solutions, not higher-dimensional vacua

Abstract

We study towers of light particles that appear in infinite-distance limits of moduli spaces of 9-dimensional $\mathcal{N}=1$ 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 $\alpha \ge \frac{1}{\sqrt{d-2}}$ 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 decompactification can lead to a running solution rather than to a higher-dimensional vacuum.