Axion Monodromy and the Weak Gravity Conjecture

TL;DR

This paper explores how the weak gravity conjecture constrains axion monodromy models, linking the cutoff scale of the theory to geometric properties of string compactifications and discussing implications for inflation and hierarchy problems.

Contribution

It proposes a minimalist constraint on axion monodromy via the weak gravity conjecture for domain walls, introducing a geometric version related to string compactifications.

Findings

The magnetic side of the conjecture sets a cutoff scale independent of potential oscillations.

String compactifications suggest a geometric weak gravity conjecture relating cycle volumes and forms.

Imposing the geometric conjecture supports the validity of the domain wall weak gravity conjecture.

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, $\Lambda^3 \sim m f M_{pl}$, 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.