Taxonomy of Infinite Distance Limits

TL;DR

This paper classifies the geometric structures of scalar charge-to-mass vectors in infinite-distance limits of quantum gravity moduli spaces, revealing constraints and potential new regions in string theory landscapes or swampland.

Contribution

It introduces a taxonomy of these vectors based on the Emergent String Conjecture, deriving rules and classifying duality frame configurations using polytopes.

Findings

Many polytopes correspond to known string compactifications

Some polytopes suggest undiscovered string theory regions

Results impose new constraints on quantum gravity moduli spaces

Abstract

The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors $(-\vec{\nabla}\log m)$ of the light towers and the analogous vector $(-\vec{\nabla}\log\Lambda_{\text{QG}})$ of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints.