Dense Geodesics, Tower Alignment, and the Sharpened Distance Conjecture

TL;DR

This paper proposes two new conjectures related to infinite distance geodesics and particle towers in moduli space, aiming to unify and sharpen existing conjectures in quantum gravity, with tests in supergravity models.

Contribution

It introduces two novel conjectures explaining the relations between geodesic density and particle towers, supported by tests in supergravity examples.

Findings

Dense sets of geodesic directions at any point in moduli space.

Existence of particle towers with specific charge-to-mass ratios along geodesics.

A sharp bound on exponentially heavy towers near infinite distance limits.

Abstract

The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1. The infinite distance geodesics passing through an arbitrary point $\phi$ in the moduli space populate a dense set of directions in the tangent space at $\phi$. 2. Along any infinite distance geodesic, there exists a tower of particles whose scalar-charge-to-mass ratio ($-\nabla \log m$) projection everywhere along the geodesic is greater than or equal to $1/\sqrt{d-2}$. I perform several nontrivial tests of these new conjectures in maximal and half-maximal supergravity examples. I also use the Tower Scalar Weak Gravity Conjecture to conjecture a sharp bound on exponentially heavy towers that accompany infinite distance limits.