Stringy Evidence for a Universal Pattern at Infinite Distance

TL;DR

This paper uncovers a universal pattern relating the variation of light tower masses and the species scale at infinite distance limits in string theory, refining the Distance Conjecture with precise bounds and broad evidence.

Contribution

It establishes a universal geometric relation in all known infinite distance limits, providing a more precise formulation of the Distance Conjecture in string theory.

Findings

Universal relation between mass variation and species scale in string theory limits

Refined bounds for exponential decay rates of towers of states

Evidence supporting the pattern across multiple string theory compactifications

Abstract

Infinite distance limits in the moduli space of a quantum gravity theory are characterized by having infinite towers of states becoming light, as dictated by the Distance Conjecture in the Swampland program. These towers imply a drastic breakdown in the perturbative regimes of the effective field theory at a quantum gravity cut-off scale known as the species scale. In this paper, we find a universal pattern satisfied in all known infinite distance limits of string theory compactifications, which relates the variation in field space of the mass of the tower and the species scale: $\frac{\vec\nabla m}{m} \cdot\frac{\vec\nabla \Lambda_{\rm sp}}{ \Lambda_{\rm sp}}=\frac{1}{d-2}$ in $d$ spacetime dimensions. This implies a more precise definition of the Distance conjecture and sharp bounds for the exponential decay rates. We provide plethora of evidence in string theory and identify some sufficient conditions that allow the pattern to hold from a bottom-up perspective.