Axion Monodromy and the Weak Gravity Conjecture
Arthur Hebecker, Fabrizio Rompineve, Alexander Westphal
TL;DR
The paper analyzes how the Weak Gravity Conjecture constrains axion monodromy models used for inflation and relaxation. It shows the electric WGC for domain-wall wiggles does not bound slow-roll, but the magnetic WGC imposes a cutoff Λ^3 ∼ m f M_pl, translating into a bound on the field range that is modest for typical decay constants. It then recasts the WGC as a geometric constraint in string compactifications, deriving cycle-volume relations that apply universally to wrapped branes without relying on dualities, and demonstrates this via explicit Type IIB reductions. The results also connect to Kaloper-Sorbo constructions and imply limits on resonant non-Gaussianity and potential eternal inflation scenarios, highlighting the geometric WGC as a foundational constraint across UV completions.
Abstract
Axions with broken discrete shift symmetry (axion monodromy) have recently played a central role both in the discussion of inflation and the `relaxion' approach to the hierarchy problem. We suggest a very minimalist way to constrain such models by the weak gravity conjecture for domain walls: While the electric side of the conjecture is always satisfied if the cosine-oscillations of the axion potential are sufficiently small, the magnetic side imposes a cutoff, $Λ^3 \sim m f M_{pl}$, independent of the height of these `wiggles'. We compare our approach with the recent related proposal by Ibanez, Montero, Uranga and Valenzuela. We also discuss the non-trivial question which version, if any, of the weak gravity conjecture for domain walls should hold. In particular, we show that string compactifications with branes of different dimensions wrapped on different cycles lead to a `geometric weak gravity conjecture' relating volumes of cycles, norms of corresponding forms and the volume of the compact space. Imposing this `geometric conjecture', e.g.~on the basis of the more widely accepted weak gravity conjecture for particles, provides at least some support for the (electric and magnetic) conjecture for domain walls.