Super-Planckian Spatial Field Variations and Quantum Gravity

TL;DR

This paper investigates super-Planckian spatial variations of scalar fields affecting gauge couplings, providing evidence that an infinite tower of states with exponentially decreasing mass emerges rapidly after the Planck scale is exceeded, consistent with quantum gravity conjectures.

Contribution

It demonstrates that super-Planckian scalar field variations induce an infinite tower of light states, supporting a key quantum gravity conjecture about the behavior of fields at large distances in field space.

Findings

Mass of states decreases exponentially with scalar field variation.

Rapid emergence of light states after crossing the Planck scale.

Supports the Weak Gravity Conjecture in spatially varying fields.

Abstract

We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.