Super-Planckian Spatial Field Variations and Quantum Gravity

TL;DR

This work investigates super‑Planckian spatial variations of a scalar field coupled to a U(1) gauge field within gravity, testing Swampland ideas via a Local Weak Gravity Conjecture (LWGC). By linking local gauge couplings to the scalar profile, the authors derive an exponential flow $g(φ) \sim g(φ_0) e^{−α Δφ/M_p}$ and connect it to the Swampland Conjecture (SC) that predicts an infinite tower of states becoming light as field space distance grows, with a finite‑$Δφ$ refinement captured by a subdominant factor $Γ$. They analyze both weakly and strongly curved backgrounds, showing that the refined SC behaviour is reached rapidly for $Δφ \gtrsim M_p$ and providing quantitative bounds on the approach via the $Γ$ factor. The results imply a tower of states with exponentially decreasing masses and argue that a Wilsonian EFT with a fixed cutoff cannot describe such spatial flows, while the magnetic LWGC remains a robust constraint. The paper discusses broader implications for cosmology, multi-field generalizations, and connections to moduli stabilization and attractor dynamics.

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.